Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards. Find the mean, variance and standard deviation of the number of kings.

Answer

N/a

Explanation

Let `X` be a random variable.
`:.X=` No. of kings obtained when two cards are drawn
`=0,1,2`
Probabiity of getting one king `p=4/52=1/13`
Probability that card drawn is not a king `q=1-p=1-1/13=12/13`
Now `P(X=0)=q.q=12/13xx12/13=144/169`
`P(X=1)=p.q+q.p=1/13xx12/13+12/13xx1/13=24/169`
`P(X=2)=p.p=1/13xx1/13=1/169`

Now Mean `barX=sumX.P(X)=26/169=2/13`
Variance `sigma^(2)=sumX^(2).P(X)-(barX)^(2)`
`=28/169-(2/13)^(2)=24/169`
and standard deviation `sigma=sqrt(24/169)=(2sqrt(6))/13`