Question

Use R statistical software to answer the following: Let X1, ..., X6 be a random sample...

Use R statistical software to answer the following:

Let X1, ..., X6 be a random sample of size n = 6 from the distribution with pdf

f(x) = x / 8 , 0 < x < 4 and 0 otherwise.

(a) Use Monte Carlo to calculate Var(Xbar), and knowing that Var(Xbar) = sigma^2 / n, what is the true value of Var(Xbar)?

## use runif() to generate samples

Math   Statistics-And-Probability   
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Answer #1

set.seed(9999)

n=10000

m={}

for(i in 1:n){

x=(16*runif(6))^0.5

m[i]=mean(x)}

var(m)*(n-1)/n

 [1] 0.1483157

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