Question

1. Generate 1000 random numbers from ??2, 5? starting with standard normal random numbers in R.

Answer 1

Suppose, we have two independent random samples from standard normal distribution.

Then,

Using this idea we will first generate a set of 2 standard normal random numbers and another set of 5 standard normal random numbers which are independent from the first set of random numbers.

Then we will square the numbers and add then to get the chi-square distribution with degrees of freedom 2 and 5 respectively. Then finally using the relation of F and Chi-square density we generate the random numbers from F(2,5) distribution. We use for loop and iterate for 1000 times to generate 1000 F(2,5) random numbers.

The R-code is given below:

f_random_number = vector()
for (i in 1:1000){
a = rnorm(2,0,1) # generate 2 standard normal random numbers
b = rnorm(5,0,1) # generate 5 standard normal random numbers
  
chi1 = sum(a^2) # chi1 follows chi-square distribution with 2 degrees of freedom
chi2 = sum(b^2) # chi1 follows chi-square distribution with 5 degrees of freedom
  
f = (chi1/2)/(chi2/5) # f is random number from F(2,5)
f_random_number[i]=f
}