Question

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.

Answer 1

Correct Answer -
Mean=6, variance = 3
`S={(1,2),(1,3),(1,4),(1,5),(2,1),(2,3),(2,4),(2,5),(3,1),(3,2),(3,4),(3,5),(4,1),(4,2),(4,3),(4,5,),(5,1),(5,2),(5,3),(5,4)}`
Then X= 3, 4, 5, 6, 7, 8 and 9.
`P(X=3)=(2)/(20)=(1)/(10),P(X=4)=(2)/(20)=(1)/(10),P(X=5)=(4)/(20)=(1)/(5),`
`P(X=6)=(4)/(20)=(1)/(5), P(X=7)=(4)/(20)=(1)/(5),P(X=8)=(2)/(20)=(1)/(10),`
`P(X=9)=(2)/(20)=(1)/(10).`