Hi this is my first post, and I'm hoping I can get some general guidance on how to solve this problem. if this isn't the place i should be asking, please direct me to the correct place.

An urn contains 2 red chips and 3 white chips. Suppose two are drawn out at random, with replacement. Let X denote the number of red chips in the sample. Find Var(X).

I understand that if it's without replacement, I would use the hypergeometric random variable formula, however, this textbook doesn't state what I should use when its with replacement. At first, I was thinking of using permutation but then I got stuck at figuring out how to find E(X).

Any help will be greatly appreciated, thank you for reading this post.

Isn't the expected value of X = 2/5 + 2/5 or 4/5? That is, on each round of two draws you expect to draw .8 red chips on average?

That should get you started, unless I'm missing something...

It's a binomial variable with n=2 and p=0.4. Var = 2*0.4*0.6

above poster has it locked down. also it sounds like you were trying to work through it w/first principles since you couldn't determine which distribution to use:

x= # of red chips

Var[x]= E[x^2] - (E[x])^2

E[x]= ∑ x*P(x) x =0, 1, 2
= 0*P(x=0) + 1*P(x=1) + 2*P(x=2)

E[x^2]= ∑ x^2*P(x)
= (0^2)*P(x=0) + (1^2)*P(x=1) + (2^2)*P(x=2)