Here, 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)}
Total Sample Space, n(S) = 20
Let random variable be X which denotes the sum of the numbers on the cards drawn.
∴ X = 3, 4, 5, 6, 7, 8, 9
At X = 3
The cards whose sum is 3 are (1,2), (2,1)
P(X) = 2/20 = 1/10
At X = 4
The cards whose sum is 4 are (1,3), (3,1)
P(X) = 2/20 = 1/10
At X = 5
The cards whose sum is 5 are (1,4),(2,3),(3,2),(4,1)
P(X) = 4/20 = 1/5
At X = 6
The cards whose sum is 6 are (1,5), (2,4),(4,2),(5,1)
P(X) = 4/20 = 1/5
At X = 7
The cards whose sum is 7 are (2,5),(3,4),(4,3),(5,2)
P(X) = 4/20 = 1/5
At X = 8
The cards whose sum is 8 are (3,5), (5,3)
P(X) = 2/20 = 1/10
At X = 9
The cards whose sum is 9 are (4,5), (5,4)
P(X) = 2/20 = 1/10
∴ Mean, E(X) = ΣXP(X)
= 6
Also,
= 39
Now,
Var X = ΣX2P(X) – [ΣXP(X)]2
= 39 – 36
= 3
