There are 5 cards numbered 1 to 5, one number on one card. Two cards are drawn at random without replacement. Let `X` denote the sum of the numbers on two cards drawn. Find the mean and variance.

Explanation

Here, sample space
S={(1,2),(2,1),(1,3),(3,1),(2,3),(3,2),(1,4),(4,1),(1,5),(5,1),(2,4),(4,2),(2,5),(5,2),(3,4),(4,3),(3,5), (5,3),(5,4),(4,5)}


`therefore n(S)=20`


Let X be the random variable denoting the sum of the numbers on two cards drawn.

`P(X=9)=frac{2}{20}`

`therefore Mean, E(X)=3 times frac{2}{20}+4 times frac{2}{20}+5 times frac{4}{20}+6 times frac{4}{20}+7 times frac{4}{20}+frac{8}{20}+9 times frac{2}{20}`

`=frac{6}{20}+ frac{8}{20}+ frac{20}{20}+ frac {24}{20}+ frac {28}{20}+ frac {16}{20}+ frac {18}{20}`

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