Discussion 7

Chapter 5 Question 15

Write a program for the user to input values for \(n\), \(p\), and \(k\), and have the program print out the exact value of \(b(n,p,k)\) and the Poisson approximation to this value.

binomial_coef <- function(n, k) {
  return(factorial(n) / (factorial(k) * factorial(n - k)))
}

binomial_dist <- function(n, p, k) {
  return(binomial_coef(n, k) * p^k * (1 - p)^(n - k))
}

poisson_approximation <- function(n, p, k) {
  lambda <- n * p
  return(exp(-lambda) * (lambda^k) / factorial(k))
}

poisson_funct <- function(n, p, k) {
  b <- binomial_dist(n, p, k)
  cat("Exact b(n, p, k): ", b, "\n")

  poisson <- poisson_approximation(n, p, k)
  cat("Poisson approx: ", poisson, "\n")
}

poisson_funct(10, 0.5, 3)

## Exact b(n, p, k):  0.1171875 
## Poisson approx:  0.1403739

Including Plots

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Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.