library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.3.3
library(gridExtra)
## Warning: package 'gridExtra' was built under R version 4.3.3

Binomické rozdelenie - nové parametre

  binom_n <- 15
  binom_p <- 0.3
  binom_mean <- binom_n * binom_p
  binom_var <- binom_n * binom_p * (1 - binom_p)
  cat("Binomial Distribution:\n")
## Binomial Distribution:
  cat("Mean:", binom_mean, "\n")
## Mean: 4.5
  cat("Variance:", binom_var, "\n\n")
## Variance: 3.15

Grafy - hustota a distribučná funkcia binomického rozdelenia

x_binom <- 0:binom_n
pmf_binom <- dbinom(x_binom, size=binom_n, prob=binom_p)
cdf_binom <- pbinom(x_binom, size=binom_n, prob=binom_p)

binom_df <- data.frame(x_binom, pmf_binom, cdf_binom)

plot_binom_pmf <- ggplot(binom_df, aes(x=x_binom)) +
  geom_bar(aes(y=pmf_binom), stat="identity", fill="blue") +
  labs(title="Binomial Distribution - PMF", y="Probability", x="x")

plot_binom_cdf <- ggplot(binom_df, aes(x=x_binom)) +
  geom_line(aes(y=cdf_binom), color="red") +
  labs(title="Binomial Distribution - CDF", y="Cumulative Probability", x="x")

Normálne rozdelenie - nové parametre

  normal_mean <- 2
  normal_sd <- 1.5
  cat("Normal Distribution:\n")
## Normal Distribution:
  cat("Mean:", normal_mean, "\n")
## Mean: 2
  cat("Variance:", normal_sd^2, "\n\n")
## Variance: 2.25

Grafy - hustota a distribučná funkcia normálneho rozdelenia

x_normal <- seq(-4, 8, length=1000)
pdf_normal <- dnorm(x_normal, mean=normal_mean, sd=normal_sd)
cdf_normal <- pnorm(x_normal, mean=normal_mean, sd=normal_sd)

normal_df <- data.frame(x_normal, pdf_normal, cdf_normal)

plot_normal_pdf <- ggplot(normal_df, aes(x=x_normal)) +
  geom_line(aes(y=pdf_normal), color="blue") +
  labs(title="Normal Distribution - PDF", y="Density", x="x")

plot_normal_cdf <- ggplot(normal_df, aes(x=x_normal)) +
  geom_line(aes(y=cdf_normal), color="red") +
  labs(title="Normal Distribution - CDF", y="Cumulative Probability", x="x")

Zobrazenie všetkých grafov vedľa seba

  grid.arrange(plot_binom_pmf, plot_binom_cdf, plot_normal_pdf, plot_normal_cdf, ncol=2)