# Thread: Help needed for Random Variable Stat Question

1. ## Help needed for Random Variable Stat Question

here is the question im not sure how to go about doing it

We know that for any random variable Y, the variance of Y is defined as
σY2 = E(Y-E(Y))2 = E(Y2) – [E(Y)]2

a) Apply this formula to the sample mean of a random sample of size n from a population with mean μ and variance σ2, and show that
E( 2) = μ2 + σ2/n

Thanks guys

2. Originally Posted by flaming
here is the question im not sure how to go about doing it

We know that for any random variable Y, the variance of Y is defined as
σY2 = E(Y-E(Y))2 = E(Y2) – [E(Y)]2

a) Apply this formula to the sample mean of a random sample of size n from a population with mean μ and variance σ2, and show that
E( 2) = μ2 + σ2/n

Thanks guys
$n(E(Y^2)-\mu^2)=\sigma^2$

There is $n$ random Y variables, hence the expectation is multiplied like so.

3. ## hey

umm can u explain to me the second part of this question im not sure when it is biased or not.

the second part is

: Is (Xbar^2) an unbiased estimator of μ2. Explain. If it is biased, what is the bias of this estimator?