Question

Write a R script that calculates the mean and variance of two random variables

X~F(m=2,n=5) and Y~F(m=10,n=5) from their density functions.

Answer 1

X~ F(m,n)

mean(x) = ;n >2

var(x) = for n > 4

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We can calculate mean and variance using R software for that we need to generate random number from F distribution.

R-script

set.seed(1234)
#x ~f(m=2,n=5)
x=rf(1000,2,5) # Generate random sample from F(2,5)
mean(x)
var(x)

# x1~ f(m=10,n=5)
set.seed(12345)
x1=rf(10000,10,5) # Generate random sample from F(10,5)
mean(x1)
var(x1)

Output-

Answer -

If X ~ F(m=2,n=5)

then ,

mean= 1.6

var= 8.2

If X~F(m=10,n=5)

mean=1.6

var=4.8

Note : some variation may come in mean and variance because we have done calculation using random sample .

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