There are 4 cards numbered 1, 3, 5 and 7, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two drawn cards. Find the mean and variance of X.

Answers (1)

given x denote the sum of the numbers on the 2 drawn cards. Then X can take values 4,6,8,10,12 and sample space $s= \left \{ \left ( 1,3 \right ) ,\left ( 1,5 \right ),\left ( 1,7 \right ),\left ( 3,1 \right ),\left ( 3,5 \right ),\left ( 3,7 \right ),\left ( 5,1 \right ),\left ( 5,3 \right ),\left ( 5,7 \right ),\left ( 7,1 \right ),\left ( 7,3 \right ),\left ( 7,5 \right )\right \}$
so the probability distribution of X is given below.
X                4            6          8         10        12
p(X)          $\frac{2}{12}$            $\frac{2}{12}$        $\frac{4}{12}$         $\frac{2}{12}$        $\frac{2}{12}$
compulation of Mean and Varience
xi             p(x = xi)        pixi                pixi^{2

4

6

8

10

12



we have

Now



Here Mean & Variance}