Two cards are drawn successively with replacement from a well shuffled deck of 52 cards. Find the mean and standard deviation of the number of aces.

Explanation

`P(X=0)=P(barA_1).P(barA_2)`
`=12/13.(12)/(13)=144/169`
`P(X=1)=P(A_1)P(barA_2)+P(barA_1)P(A_2)`
`=1/13xx12/13+12/13.(1)/(13)=24/169`
`P(X=2)=P(A_1).P(A_2)`
`=1/13.(1)/(13)=1/169`

`Mean=sum_(i=1)^(n)X_iP_i=26/169`
`variance =sum_(n=1)^(n)X_i^2P_i-(sum_(i=1)^(n)X_iP_i)^2=24/169`
`"Standard deviation"=sqrt(Var)=(2sqrt6)/13`