restructured file organisation and finished assignment 2a

Oblig/1c/Oppg1RScript.R

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+#Hvor mange måter kan du plukke 5 elementer fra 12
+#når trekket er...
+
+n <- 12
+k <- 5
+
+#a) ordnet, med tilbakelegging
+n^k
+
+#b) uordnet, med tilbakelegging
+choose((n + k - 1), k)
+
+#c) ordnet, uten tilbakelegging
+factorial(n) / factorial(n - k)
+
+#d) uordnet, uten tilbakelegging
+choose(n, k)
+
+#Eksempel på a) - PIN-kode med 5 siffer. Man kan gjenbruke ett siffer flere
+#ganger
+
+#Eksempel på b) - Velg 5 is-kuler fra et utvalg av 5 smaker. Hver kule trenger
+#ikke være unik
+
+#Eksempel på c) - Velg 5 studenter fra en gruppe på 12 og sorter dem etter alder
+
+#Eksempel på d) - Trekk 5 kort fra en bunke på 12 uten å legge dem tilbake

Oblig/1c/Oppg2RScript.R

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+#Twist-posen
+#a) Du skal rydde opp etter en fest, og finner en Twist-pose med kun 7 kokos 
+#og 13 lakris igjen. Du plukker en tilfeldig twist. Hva er sannsynligheten
+#for at den blir en kokos?
+kokos <- 7
+lakris <- 13
+total = kokos + lakris
+
+P_kokos = kokos / total
+
+
+#b) Du liker verken lakris eller kokos, så du legger den du har plukket tilbake
+#i posen for å plukke en ny. Du prøver deg slik 5 ganger, og legger tilbake 
+#for hver gang. Lag stoplediagram over sannsynligheten for at du har plukket
+#kokos respektivt 0, 1, 2, 3, 4 og 5 ganger
+N <- total
+S <- kokos
+p <- S / N
+n <- 5
+
+#Formel 4.2.3 i formelheftet
+ProbComb = function(k){
+  choose(n, k) * (p^k) * (1 - p)^(n - k)
+}
+ProbComb(0)
+ProbComb(1)
+ProbComb(2)
+ProbComb(3)
+ProbComb(4)
+ProbComb(5)
+
+
+
+
+#Litt senere på morran er du så sultern at selv kokos og lakris går an, så
+#du plukker 5 twist og spiser dem. Lag stolpediagram over sannsynligheten for
+#at du spiser respektive 0, 1, 2, 3, 4 og 5 kokos
+ProbCombNoReplace = function(k){
+  (choose(S, k) * choose((N - S), n - k) / choose(N, n))
+}
+ProbCombNoReplace(0)
+ProbCombNoReplace(1)
+ProbCombNoReplace(2)
+ProbCombNoReplace(3)
+ProbCombNoReplace(4)
+ProbCombNoReplace(5)
+
+
+#Diagrammer
+k_values <- 0:n
+probs_binom <- sapply(k_values, ProbComb)
+probs_hyper <- sapply(k_values, ProbCombNoReplace)
+
+max_b <- max(probs_binom)
+max_h <- max(probs_hyper)
+
+max_y <- max(max_b, max_h)
+
+ylim_val <- c(0, max_y * 1.1)
+
+
+par(mfrow = c(1, 2))
+
+barplot(probs_binom, names.arg = k_values, col = "steelblue",
+        ylim = ylim_val, xlab = "Antall kokos", ylab = "Sannsynlighet", 
+        main = "Med tilbakelegging")
+
+barplot(probs_hyper, names.arg = k_values, col = "darkorange", 
+        ylim = ylim_val, xlab = "Antall kokos", ylab = "Sannsynlighet", 
+        main = "Uten tilbakelegging")
+par(mfrow = c(1, 1))
+

Oblig/1c/Oppg4RScript.R

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+#4a
+myChoose = function(n, k){
+  factorial(n) / (factorial(k) * factorial(n - k))
+}
+
+choose(4, 2)
+myChoose(4, 2)
+
+
+#4b
+#Definerer funksjonen bd med parameter n
+bd = function(n){
+  
+  #Setter antall "frie" dager
+  dager = 365 + 1 - 1:n
+  
+  #Deler antall "frie" dager på antall
+  #dager i et år - gir et desimaltall som
+  #ganges med 100 for å få den eksakte prosentverdien
+  #for sannsynligheten at ingen i samme set har 
+  #samme bursdag
+  sjanser = dager / 365
+  
+  #Utfører utregningen og lagrer resultatet til 
+  #variablen output
+  output = prod(sjanser)
+  
+  #Printer resultatet
+  output
+}
+#Regner ut og printer sannsynligheten for at 
+#to personer i samme set har samme bursdag
+#Vi gjør "1 - bd()" for å finne sannsynligheten
+1 - bd(22)
+1 - bd(23)
+#Denne funksjonen regner sannsynligheten for at ingen
+#personer i samme set har bursdag på samme dag
+#Bursdagsparadokset er et berømt statistikk eksempel
+
+
+#4c
+#Setter startpunktet til en Random Number Generator(RNG)
+set.seed(314)
+
+#Lager en mengde / sekvens fra 3 til 27 (3, 4, 5, ..., 27)
+base = 3:27
+
+#Trekker 14 tall fra sekvensen "base" med tilbakelegging
+a = sample(base, 14, replace=TRUE)
+
+
+#4d
+totalSum = 0
+for(verdi in a){
+  totalSum = totalSum + verdi
+}
+totalSum
+sum(a)
+
+
+#4e
+totalProd = 1
+for (verdi in a) {
+  totalProd = totalProd * verdi
+}
+totalProd
+prod(a)
+
+
+#4f
+#Med tilbakelegging - kan få samme verdi flere gange
+a = sample(base, 14, replace=TRUE)
+sort(a)
+
+#Uten tilbakelegging - kan kun få atomære verdier
+a = sample(base, 14, replace=FALSE)
+sort(a)
+
+
+
+
+
+
+

Oblig/1c/kokosDiagram.svg

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Oblig/2a/2a.Rproj

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+Version: 1.0
+
+RestoreWorkspace: Default
+SaveWorkspace: Default
+AlwaysSaveHistory: Default
+
+EnableCodeIndexing: Yes
+UseSpacesForTab: Yes
+NumSpacesForTab: 2
+Encoding: UTF-8
+
+RnwWeave: Sweave
+LaTeX: pdfLaTeX

Oblig/2a/markeringAvIntervallestimat.R

@@ -0,0 +1,473 @@
+# ============================================================
+# Oppgave 3g -- Symmetrisk 90% intervallestimat
+# Genererer pdf, CDF og iCDF for alle 8 grupper
+# med markerte 5. og 95. prosentiler
+# ============================================================
+
+
+install.packages(c("ggplot2", "patchwork", "scales"))
+
+library(ggplot2)
+library(patchwork)
+
+col_curve <- "red3"
+col_shade <- scales::alpha("red3", 0.2)
+col_mark  <- "steelblue"
+
+theme_oblig <- theme_classic() +
+  theme(
+    axis.title = element_text(size = 9),
+    axis.text  = element_text(size = 8),
+    plot.title = element_text(size = 10, face = "bold")
+  )
+
+# Hjelpefunksjon for segmenter (unngaar advarsler fra geom_segment med aes)
+seg <- function(x1, y1, x2, y2, ...) {
+  annotate("segment", x = x1, xend = x2, y = y1, yend = y2, ...)
+}
+
+# Lagringsfunksjon med feilhåndtering
+lagre_gruppe <- function(navn, pdf_plot, cdf_plot, icdf_plot) {
+  tryCatch({
+    kombinert <- pdf_plot + cdf_plot + icdf_plot +
+      plot_annotation(
+        title = paste("Gruppe", navn),
+        theme = theme(plot.title = element_text(size = 12, face = "bold"))
+      )
+    ggsave(paste0("gruppe_", navn, ".png"), kombinert,
+           width = 12, height = 4, dpi = 150)
+    message("OK: gruppe_", navn, ".png lagret")
+  }, error = function(e) {
+    message("FEIL gruppe ", navn, ": ", conditionMessage(e))
+  })
+}
+
+# x-vektor for kontinuerlige fordelinger (brukes av d, e, f, g, h)
+x_kont <- seq(0, 10, length.out = 500)
+
+# ============================================================
+# GRUPPE a -- Diskret, ujevn
+# ============================================================
+tryCatch({
+  vals_a <- 1:10
+  prob_a <- c(0.03, 0.08, 0.09, 0.03, 0.03, 0.065, 0.14, 0.21, 0.19, 0.075)
+  prob_a <- prob_a / sum(prob_a)
+  cdf_a  <- cumsum(prob_a)
+  p05_a  <- min(vals_a[cdf_a >= 0.05])
+  p95_a  <- min(vals_a[cdf_a >= 0.95])
+  df_a   <- data.frame(x = vals_a, f = prob_a, F = cdf_a)
+  
+  pdf_a <- ggplot(df_a, aes(x, f)) +
+    geom_bar(stat = "identity",
+             fill  = ifelse(vals_a >= p05_a & vals_a <= p95_a, col_shade, "white"),
+             color = col_curve, width = 0.4) +
+    geom_vline(xintercept = c(p05_a, p95_a), color = col_mark,
+               linetype = "dashed", linewidth = 0.8) +
+    annotate("text", x = p05_a, y = max(prob_a) * 0.95,
+             label = paste0("x[0.05]==", p05_a), parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    annotate("text", x = p95_a, y = max(prob_a) * 0.95,
+             label = paste0("x[0.95]==", p95_a), parse = TRUE,
+             hjust = 1.1, size = 3, color = col_mark) +
+    scale_x_continuous(breaks = 1:10) +
+    labs(title = "pdf a", x = "x", y = "f(x)") + theme_oblig
+  
+  cdf_a_plot <- ggplot(df_a, aes(x, F)) +
+    geom_step(color = col_curve, linewidth = 0.8) +
+    geom_point(color = col_curve, size = 2) +
+    geom_hline(yintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
+    seg(p05_a, 0, p05_a, 0.05, color = col_mark, linewidth = 0.8) +
+    seg(p95_a, 0, p95_a, 0.95, color = col_mark, linewidth = 0.8) +
+    annotate("text", x = p05_a, y = 0.08,
+             label = paste0("x[0.05]==", p05_a), parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    annotate("text", x = p95_a, y = 0.92,
+             label = paste0("x[0.95]==", p95_a), parse = TRUE,
+             hjust = 1.1, size = 3, color = col_mark) +
+    scale_x_continuous(breaks = 1:10) +
+    labs(title = "CDF E", x = "x", y = "F(x)") + theme_oblig
+  
+  icdf_a_df <- data.frame(p = c(0, cdf_a), x = c(vals_a[1], vals_a))
+  icdf_a_plot <- ggplot(icdf_a_df, aes(p, x)) +
+    geom_step(color = col_curve, linewidth = 0.8, direction = "vh") +
+    geom_vline(xintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
+    annotate("text", x = 0.05, y = 9.5, label = "p==0.05", parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    annotate("text", x = 0.95, y = 9.5, label = "p==0.95", parse = TRUE,
+             hjust = 1.1, size = 3, color = col_mark) +
+    scale_y_continuous(breaks = 1:10) +
+    labs(title = "iCDF (a)", x = "p", y = "F-inv(p)") + theme_oblig
+  
+  lagre_gruppe("a", pdf_a, cdf_a_plot, icdf_a_plot)
+}, error = function(e) message("FEIL gruppe a: ", e$message))
+
+# ============================================================
+# GRUPPE b -- Diskret, synkende
+# ============================================================
+tryCatch({
+  vals_b <- 1:10
+  prob_b <- c(0.40, 0.25, 0.13, 0.08, 0.05, 0.04, 0.02, 0.015, 0.01, 0.005)
+  prob_b <- prob_b / sum(prob_b)
+  cdf_b  <- cumsum(prob_b)
+  p05_b  <- min(vals_b[cdf_b >= 0.05])
+  p95_b  <- min(vals_b[cdf_b >= 0.95])
+  df_b   <- data.frame(x = vals_b, f = prob_b, F = cdf_b)
+  
+  pdf_b <- ggplot(df_b, aes(x, f)) +
+    geom_bar(stat = "identity",
+             fill  = ifelse(vals_b >= p05_b & vals_b <= p95_b, col_shade, "white"),
+             color = col_curve, width = 0.4) +
+    geom_vline(xintercept = c(p05_b, p95_b), color = col_mark,
+               linetype = "dashed", linewidth = 0.8) +
+    annotate("text", x = p05_b, y = max(prob_b) * 0.95,
+             label = paste0("x[0.05]==", p05_b), parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    annotate("text", x = p95_b, y = max(prob_b) * 0.70,
+             label = paste0("x[0.95]==", p95_b), parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    scale_x_continuous(breaks = 1:10) +
+    labs(title = "pdf b", x = "x", y = "f(x)") + theme_oblig
+  
+  cdf_b_plot <- ggplot(df_b, aes(x, F)) +
+    geom_step(color = col_curve, linewidth = 0.8) +
+    geom_point(color = col_curve, size = 2) +
+    geom_hline(yintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
+    seg(p05_b, 0, p05_b, 0.05, color = col_mark, linewidth = 0.8) +
+    seg(p95_b, 0, p95_b, 0.95, color = col_mark, linewidth = 0.8) +
+    annotate("text", x = p05_b, y = 0.08,
+             label = paste0("x[0.05]==", p05_b), parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    annotate("text", x = p95_b, y = 0.92,
+             label = paste0("x[0.95]==", p95_b), parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    scale_x_continuous(breaks = 1:10) +
+    labs(title = "CDF C", x = "x", y = "F(x)") + theme_oblig
+  
+  icdf_b_df <- data.frame(p = c(0, cdf_b), x = c(vals_b[1], vals_b))
+  icdf_b_plot <- ggplot(icdf_b_df, aes(p, x)) +
+    geom_step(color = col_curve, linewidth = 0.8, direction = "vh") +
+    geom_vline(xintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
+    annotate("text", x = 0.05, y = 9.5, label = "p==0.05", parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    annotate("text", x = 0.95, y = 9.5, label = "p==0.95", parse = TRUE,
+             hjust = 1.1, size = 3, color = col_mark) +
+    scale_y_continuous(breaks = 1:10) +
+    labs(title = "iCDF (b)", x = "p", y = "F-inv(p)") + theme_oblig
+  
+  lagre_gruppe("b", pdf_b, cdf_b_plot, icdf_b_plot)
+}, error = function(e) message("FEIL gruppe b: ", e$message))
+
+# ============================================================
+# GRUPPE c -- Diskret, uniform
+# ============================================================
+tryCatch({
+  vals_c <- 1:10
+  prob_c <- rep(0.1, 10)
+  cdf_c  <- cumsum(prob_c)
+  p05_c  <- min(vals_c[cdf_c >= 0.05])
+  p95_c  <- min(vals_c[cdf_c >= 0.95])
+  df_c   <- data.frame(x = vals_c, f = prob_c, F = cdf_c)
+  
+  pdf_c <- ggplot(df_c, aes(x, f)) +
+    geom_bar(stat = "identity", fill = col_shade, color = col_curve, width = 0.4) +
+    geom_vline(xintercept = c(p05_c, p95_c), color = col_mark,
+               linetype = "dashed", linewidth = 0.8) +
+    annotate("text", x = p05_c, y = 0.13,
+             label = paste0("x[0.05]==", p05_c), parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    annotate("text", x = p95_c, y = 0.13,
+             label = paste0("x[0.95]==", p95_c), parse = TRUE,
+             hjust = 1.1, size = 3, color = col_mark) +
+    scale_x_continuous(breaks = 1:10) + ylim(0, 0.15) +
+    labs(title = "pdf c", x = "x", y = "f(x)") + theme_oblig
+  
+  cdf_c_plot <- ggplot(df_c, aes(x, F)) +
+    geom_step(color = col_curve, linewidth = 0.8) +
+    geom_point(color = col_curve, size = 2) +
+    geom_hline(yintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
+    seg(p05_c, 0, p05_c, 0.05, color = col_mark, linewidth = 0.8) +
+    seg(p95_c, 0, p95_c, 0.95, color = col_mark, linewidth = 0.8) +
+    annotate("text", x = p05_c, y = 0.08,
+             label = paste0("x[0.05]==", p05_c), parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    annotate("text", x = p95_c, y = 0.92,
+             label = paste0("x[0.95]==", p95_c), parse = TRUE,
+             hjust = 1.1, size = 3, color = col_mark) +
+    scale_x_continuous(breaks = 1:10) +
+    labs(title = "CDF G", x = "x", y = "F(x)") + theme_oblig
+  
+  icdf_c_df <- data.frame(p = c(0, cdf_c), x = c(vals_c[1], vals_c))
+  icdf_c_plot <- ggplot(icdf_c_df, aes(p, x)) +
+    geom_step(color = col_curve, linewidth = 0.8, direction = "vh") +
+    geom_vline(xintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
+    annotate("text", x = 0.05, y = 9.5, label = "p==0.05", parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    annotate("text", x = 0.95, y = 9.5, label = "p==0.95", parse = TRUE,
+             hjust = 1.1, size = 3, color = col_mark) +
+    scale_y_continuous(breaks = 1:10) +
+    labs(title = "iCDF (c)", x = "p", y = "F-inv(p)") + theme_oblig
+  
+  lagre_gruppe("c", pdf_c, cdf_c_plot, icdf_c_plot)
+}, error = function(e) message("FEIL gruppe c: ", e$message))
+
+# ============================================================
+# GRUPPE d -- Kontinuerlig, bimodal
+# ============================================================
+tryCatch({
+  pdf_d_fun <- function(x) 0.55 * dnorm(x, 2, 0.9) + 0.45 * dnorm(x, 6, 1.2)
+  cdf_d_fun <- function(x) 0.55 * pnorm(x, 2, 0.9) + 0.45 * pnorm(x, 6, 1.2)
+  
+  p05_d <- uniroot(function(x) cdf_d_fun(x) - 0.05, c(-5, 15))$root
+  p95_d <- uniroot(function(x) cdf_d_fun(x) - 0.95, c(-5, 15))$root
+  df_d  <- data.frame(x = x_kont, f = pdf_d_fun(x_kont), F = cdf_d_fun(x_kont))
+  
+  # iCDF via approxfun (unngaar uniroot-feil)
+  x_vid     <- seq(-3, 13, length.out = 3000)
+  icdf_d_fn <- approxfun(cdf_d_fun(x_vid), x_vid, rule = 2)
+  p_seq_d   <- seq(0.001, 0.999, length.out = 400)
+  df_icdf_d <- data.frame(p = p_seq_d, x = icdf_d_fn(p_seq_d))
+  
+  pdf_d <- ggplot(df_d, aes(x, f)) +
+    geom_area(data = subset(df_d, x >= p05_d & x <= p95_d), fill = col_shade) +
+    geom_line(color = col_curve, linewidth = 0.8) +
+    geom_vline(xintercept = c(p05_d, p95_d), color = col_mark,
+               linetype = "dashed", linewidth = 0.8) +
+    annotate("text", x = p05_d, y = max(df_d$f) * 0.95,
+             label = sprintf("x[0.05]==%.2f", p05_d), parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    annotate("text", x = p95_d, y = max(df_d$f) * 0.95,
+             label = sprintf("x[0.95]==%.2f", p95_d), parse = TRUE,
+             hjust = 1.1, size = 3, color = col_mark) +
+    labs(title = "pdf d", x = "x", y = "f(x)") + theme_oblig
+  
+  cdf_d_plot <- ggplot(df_d, aes(x, F)) +
+    geom_line(color = col_curve, linewidth = 0.8) +
+    geom_hline(yintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
+    seg(p05_d, 0, p05_d, 0.05, color = col_mark, linewidth = 0.8) +
+    seg(p95_d, 0, p95_d, 0.95, color = col_mark, linewidth = 0.8) +
+    annotate("text", x = p05_d, y = 0.08,
+             label = sprintf("%.2f", p05_d), hjust = -0.2, size = 3, color = col_mark) +
+    annotate("text", x = p95_d, y = 0.92,
+             label = sprintf("%.2f", p95_d), hjust = 1.2, size = 3, color = col_mark) +
+    labs(title = "CDF A", x = "x", y = "F(x)") + theme_oblig
+  
+  icdf_d_plot <- ggplot(df_icdf_d, aes(p, x)) +
+    geom_line(color = col_curve, linewidth = 0.8) +
+    geom_vline(xintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
+    seg(0.05, 0, 0.05, p05_d, color = col_mark, linewidth = 0.8) +
+    seg(0.95, 0, 0.95, p95_d, color = col_mark, linewidth = 0.8) +
+    annotate("text", x = 0.05, y = 9.5, label = "p==0.05", parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    annotate("text", x = 0.95, y = 9.5, label = "p==0.95", parse = TRUE,
+             hjust = 1.1, size = 3, color = col_mark) +
+    labs(title = "iCDF (d)", x = "p", y = "F-inv(p)") + theme_oblig
+  
+  lagre_gruppe("d", pdf_d, cdf_d_plot, icdf_d_plot)
+}, error = function(e) message("FEIL gruppe d: ", e$message))
+
+# ============================================================
+# GRUPPE e -- Normal(5, 1.5)
+# ============================================================
+tryCatch({
+  mu_e <- 5; sigma_e <- 1.5
+  p05_e <- qnorm(0.05, mu_e, sigma_e)
+  p95_e <- qnorm(0.95, mu_e, sigma_e)
+  df_e  <- data.frame(x = x_kont,
+                      f = dnorm(x_kont, mu_e, sigma_e),
+                      F = pnorm(x_kont, mu_e, sigma_e))
+  p_seq_e   <- seq(0.001, 0.999, length.out = 300)
+  df_icdf_e <- data.frame(p = p_seq_e, x = qnorm(p_seq_e, mu_e, sigma_e))
+  
+  pdf_e <- ggplot(df_e, aes(x, f)) +
+    geom_area(data = subset(df_e, x >= p05_e & x <= p95_e), fill = col_shade) +
+    geom_line(color = col_curve, linewidth = 0.8) +
+    geom_vline(xintercept = c(p05_e, p95_e), color = col_mark,
+               linetype = "dashed", linewidth = 0.8) +
+    annotate("text", x = p05_e, y = max(df_e$f) * 0.95,
+             label = sprintf("x[0.05]==%.2f", p05_e), parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    annotate("text", x = p95_e, y = max(df_e$f) * 0.95,
+             label = sprintf("x[0.95]==%.2f", p95_e), parse = TRUE,
+             hjust = 1.1, size = 3, color = col_mark) +
+    labs(title = "pdf e", x = "x", y = "f(x)") + theme_oblig
+  
+  cdf_e_plot <- ggplot(df_e, aes(x, F)) +
+    geom_line(color = col_curve, linewidth = 0.8) +
+    geom_hline(yintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
+    seg(p05_e, 0, p05_e, 0.05, color = col_mark, linewidth = 0.8) +
+    seg(p95_e, 0, p95_e, 0.95, color = col_mark, linewidth = 0.8) +
+    annotate("text", x = p05_e, y = 0.08,
+             label = sprintf("%.2f", p05_e), hjust = -0.2, size = 3, color = col_mark) +
+    annotate("text", x = p95_e, y = 0.92,
+             label = sprintf("%.2f", p95_e), hjust = 1.2, size = 3, color = col_mark) +
+    labs(title = "CDF H", x = "x", y = "F(x)") + theme_oblig
+  
+  icdf_e_plot <- ggplot(df_icdf_e, aes(p, x)) +
+    geom_line(color = col_curve, linewidth = 0.8) +
+    geom_vline(xintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
+    seg(0.05, 0, 0.05, p05_e, color = col_mark, linewidth = 0.8) +
+    seg(0.95, 0, 0.95, p95_e, color = col_mark, linewidth = 0.8) +
+    annotate("text", x = 0.05, y = 9,
+             label = sprintf("%.2f", p05_e), hjust = -0.2, size = 3, color = col_mark) +
+    annotate("text", x = 0.95, y = 9,
+             label = sprintf("%.2f", p95_e), hjust = 1.2, size = 3, color = col_mark) +
+    labs(title = "iCDF (e)", x = "p", y = "F-inv(p)") + theme_oblig
+  
+  lagre_gruppe("e", pdf_e, cdf_e_plot, icdf_e_plot)
+}, error = function(e) message("FEIL gruppe e: ", e$message))
+
+# ============================================================
+# GRUPPE f -- Uniform(0, 10)
+# ============================================================
+tryCatch({
+  p05_f <- qunif(0.05, 0, 10)
+  p95_f <- qunif(0.95, 0, 10)
+  df_f  <- data.frame(x = x_kont,
+                      f = dunif(x_kont, 0, 10),
+                      F = punif(x_kont, 0, 10))
+  p_seq_f   <- seq(0, 1, length.out = 300)
+  df_icdf_f <- data.frame(p = p_seq_f, x = qunif(p_seq_f, 0, 10))
+  
+  pdf_f <- ggplot(df_f, aes(x, f)) +
+    geom_area(data = subset(df_f, x >= p05_f & x <= p95_f), fill = col_shade) +
+    geom_line(color = col_curve, linewidth = 0.8) +
+    geom_vline(xintercept = c(p05_f, p95_f), color = col_mark,
+               linetype = "dashed", linewidth = 0.8) +
+    annotate("text", x = p05_f, y = 0.13,
+             label = sprintf("x[0.05]==%.1f", p05_f), parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    annotate("text", x = p95_f, y = 0.13,
+             label = sprintf("x[0.95]==%.1f", p95_f), parse = TRUE,
+             hjust = 1.1, size = 3, color = col_mark) +
+    ylim(0, 0.15) +
+    labs(title = "pdf f", x = "x", y = "f(x)") + theme_oblig
+  
+  cdf_f_plot <- ggplot(df_f, aes(x, F)) +
+    geom_line(color = col_curve, linewidth = 0.8) +
+    geom_hline(yintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
+    seg(p05_f, 0, p05_f, 0.05, color = col_mark, linewidth = 0.8) +
+    seg(p95_f, 0, p95_f, 0.95, color = col_mark, linewidth = 0.8) +
+    annotate("text", x = p05_f, y = 0.08,
+             label = sprintf("%.1f", p05_f), hjust = -0.3, size = 3, color = col_mark) +
+    annotate("text", x = p95_f, y = 0.92,
+             label = sprintf("%.1f", p95_f), hjust = 1.3, size = 3, color = col_mark) +
+    labs(title = "CDF B", x = "x", y = "F(x)") + theme_oblig
+  
+  icdf_f_plot <- ggplot(df_icdf_f, aes(p, x)) +
+    geom_line(color = col_curve, linewidth = 0.8) +
+    geom_vline(xintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
+    seg(0.05, 0, 0.05, p05_f, color = col_mark, linewidth = 0.8) +
+    seg(0.95, 0, 0.95, p95_f, color = col_mark, linewidth = 0.8) +
+    annotate("text", x = 0.05, y = 9,
+             label = sprintf("%.1f", p05_f), hjust = -0.3, size = 3, color = col_mark) +
+    annotate("text", x = 0.95, y = 9,
+             label = sprintf("%.1f", p95_f), hjust = 1.3, size = 3, color = col_mark) +
+    labs(title = "iCDF (f)", x = "p", y = "F-inv(p)") + theme_oblig
+  
+  lagre_gruppe("f", pdf_f, cdf_f_plot, icdf_f_plot)
+}, error = function(e) message("FEIL gruppe f: ", e$message))
+
+# ============================================================
+# GRUPPE g -- Triangel(0, 10). F(x) = x^2/100
+# ============================================================
+tryCatch({
+  p05_g   <- 10 * sqrt(0.05)
+  p95_g   <- 10 * sqrt(0.95)
+  pdf_g_f <- function(x) ifelse(x >= 0 & x <= 10, x / 50, 0)
+  cdf_g_f <- function(x) ifelse(x < 0, 0, ifelse(x > 10, 1, x^2 / 100))
+  df_g    <- data.frame(x = x_kont, f = pdf_g_f(x_kont), F = cdf_g_f(x_kont))
+  
+  p_seq_g   <- seq(0, 1, length.out = 300)
+  df_icdf_g <- data.frame(p = p_seq_g, x = 10 * sqrt(p_seq_g))
+  
+  pdf_g <- ggplot(df_g, aes(x, f)) +
+    geom_area(data = subset(df_g, x >= p05_g & x <= p95_g), fill = col_shade) +
+    geom_line(color = col_curve, linewidth = 0.8) +
+    geom_vline(xintercept = c(p05_g, p95_g), color = col_mark,
+               linetype = "dashed", linewidth = 0.8) +
+    annotate("text", x = p05_g, y = 0.23,
+             label = sprintf("x[0.05]==%.2f", p05_g), parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    annotate("text", x = p95_g, y = 0.23,
+             label = sprintf("x[0.95]==%.2f", p95_g), parse = TRUE,
+             hjust = 1.1, size = 3, color = col_mark) +
+    labs(title = "pdf g", x = "x", y = "f(x)") + theme_oblig
+  
+  cdf_g_plot <- ggplot(df_g, aes(x, F)) +
+    geom_line(color = col_curve, linewidth = 0.8) +
+    geom_hline(yintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
+    seg(p05_g, 0, p05_g, 0.05, color = col_mark, linewidth = 0.8) +
+    seg(p95_g, 0, p95_g, 0.95, color = col_mark, linewidth = 0.8) +
+    annotate("text", x = p05_g, y = 0.08,
+             label = sprintf("%.2f", p05_g), hjust = -0.2, size = 3, color = col_mark) +
+    annotate("text", x = p95_g, y = 0.92,
+             label = sprintf("%.2f", p95_g), hjust = 1.2, size = 3, color = col_mark) +
+    labs(title = "CDF F", x = "x", y = "F(x)") + theme_oblig
+  
+  icdf_g_plot <- ggplot(df_icdf_g, aes(p, x)) +
+    geom_line(color = col_curve, linewidth = 0.8) +
+    geom_vline(xintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
+    seg(0.05, 0, 0.05, p05_g, color = col_mark, linewidth = 0.8) +
+    seg(0.95, 0, 0.95, p95_g, color = col_mark, linewidth = 0.8) +
+    annotate("text", x = 0.05, y = 9.5,
+             label = sprintf("%.2f", p05_g), hjust = -0.2, size = 3, color = col_mark) +
+    annotate("text", x = 0.95, y = 9.5,
+             label = sprintf("%.2f", p95_g), hjust = 1.2, size = 3, color = col_mark) +
+    labs(title = "iCDF (g)", x = "p", y = "F-inv(p)") + theme_oblig
+  
+  lagre_gruppe("g", pdf_g, cdf_g_plot, icdf_g_plot)
+}, error = function(e) message("FEIL gruppe g: ", e$message))
+
+# ============================================================
+# GRUPPE h -- Eksponensiell(rate=0.2)
+# 95. prosentil er ~15, utenfor x-aksen [0,10]
+# ============================================================
+tryCatch({
+  rate_h <- 0.2
+  p05_h  <- qexp(0.05, rate_h)
+  p95_h  <- qexp(0.95, rate_h)
+  df_h   <- data.frame(x = x_kont,
+                       f = dexp(x_kont, rate_h),
+                       F = pexp(x_kont, rate_h))
+  p_seq_h   <- seq(0.001, 0.99, length.out = 300)
+  df_icdf_h <- data.frame(p = p_seq_h, x = qexp(p_seq_h, rate_h))
+  
+  pdf_h <- ggplot(df_h, aes(x, f)) +
+    geom_area(data = subset(df_h, x >= p05_h), fill = col_shade) +
+    geom_line(color = col_curve, linewidth = 0.8) +
+    geom_vline(xintercept = p05_h, color = col_mark,
+               linetype = "dashed", linewidth = 0.8) +
+    annotate("text", x = p05_h, y = max(df_h$f) * 0.9,
+             label = sprintf("x[0.05]==%.2f", p05_h), parse = TRUE,
+             hjust = -0.1, size = 3, color = col_mark) +
+    annotate("text", x = 4.5, y = max(df_h$f) * 0.45,
+             label = "x[0.95] == 14.98 (utenfor)", parse = FALSE,
+             hjust = 0, size = 3, color = col_mark) +
+    labs(title = "pdf h", x = "x", y = "f(x)") + theme_oblig
+  
+  cdf_h_plot <- ggplot(df_h, aes(x, F)) +
+    geom_line(color = col_curve, linewidth = 0.8) +
+    geom_hline(yintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
+    seg(p05_h, 0, p05_h, 0.05, color = col_mark, linewidth = 0.8) +
+    annotate("text", x = p05_h, y = 0.08,
+             label = sprintf("%.2f", p05_h), hjust = -0.2, size = 3, color = col_mark) +
+    annotate("text", x = 4, y = 0.95,
+             label = "x[0.95] = 14.98 (utenfor)", parse = FALSE,
+             hjust = 0, size = 3, color = col_mark) +
+    labs(title = "CDF D", x = "x", y = "F(x)") + theme_oblig
+  
+  icdf_h_plot <- ggplot(df_icdf_h, aes(p, x)) +
+    geom_line(color = col_curve, linewidth = 0.8) +
+    geom_vline(xintercept = c(0.05, 0.95), color = col_mark, linetype = "dashed") +
+    seg(0.05, 0, 0.05, p05_h, color = col_mark, linewidth = 0.8) +
+    seg(0.95, 0, 0.95, p95_h, color = col_mark, linewidth = 0.8) +
+    annotate("text", x = 0.05, y = max(df_icdf_h$x) * 0.9,
+             label = sprintf("%.2f", p05_h), hjust = -0.2, size = 3, color = col_mark) +
+    annotate("text", x = 0.95, y = max(df_icdf_h$x) * 0.9,
+             label = sprintf("%.2f", p95_h), hjust = 1.2, size = 3, color = col_mark) +
+    labs(title = "iCDF (h)", x = "p", y = "F-inv(p)") + theme_oblig
+  
+  lagre_gruppe("h", pdf_h, cdf_h_plot, icdf_h_plot)
+}, error = function(e) message("FEIL gruppe h: ", e$message))
+
+message("\nFerdig! Sjekk konsollen for eventuelle feilmeldinger.")