Q. 14. Find the expected value of the number X shown on the face of a dice, when the dice is thrown. The dice is unbiased. (Note : Face value of a dice is 1, 2, 3, 4, 5 or 6) (Jan. 2001)

Solution. X can take values 1, 2, 3, 4, 5, 6 each with a probability 1/6.
E(X) = x_i P (x = x_i)
or E(X) = [1 X (1/6)] + [2 X (1/6)] + [3 X (1/6)] + [4 X (1/6)] + [5 X (1/6)] + [6 X (1/6)]
or E(X) = 3.5

Q. 15. A consignment of eight similar microcomputers to retail outlet contains 3 that are defective. If a firm makes a random purchase of 2 of these computers, find the probability distribution for the number of defectives. (Dec. 98)

Solution. Let X = random variable (i.e., random purchase of 2 defective computers)
So, x can take the values (0, 1, 2)

F[X = x = 0] = P[x = 0] = (³C₀ X ⁵C₂)/⁸C₂
= 0.36
Therefore, F[x = 0] = 0.36

F[X = x = 1] = P[x = 1] = (³C₁ X ⁵C₁)/⁸C₂
= 0.53
Therefore, F[x = 1] = 0.53

F[X = x = 2] = P[x = 2] = (³C₂ X ⁵C₀)/⁸C₂
= 0.11
Therefore, F[x = 2] = 0.11