Hello,

Let Xx be the random variable denoting the number of aces when 2 cards are drawn,with replacement from well-shuffled pack of 52 cards.

Xx takes the values 0,1,2

P(X=0) = Probability of no aces

= 144 / 169

P(X=1) = Probability of 1ace

= 24 / 169

P(X=2) = Probability of 2 aces

= 1 / 169

So, Mean ( X ) = 0 x ( 144 / 169 ) + 1 x ( 24 / 169 ) + 2 x ( 1 / 169 )

So, Mean ( X ) = 26 / 169

So, Mean ( X ) = 2 / 13

Now, Var ( X ) = E ( X^2 ) - [ E ( X ) ]^2

E ( X^2 ) = Sum. of xi^2 Pi = 28 / 169

So, Var ( X ) = ( 28 /169 ) - ( 4 / 169 )

So, Var ( X ) = 24 / 169

Best Wishes