Question

State which of the following are not the probability distributions of a random variable. Give reasons for your answer. (i) X 0 1 2 P (X) 0.4 0.4 0.2 (ii) X 0 1 2 3 4 P (X) 0.1 0.5 0.2 − 0.1 0.3 (iii) Y −1 0 1 P (Y) 0.6 0.1 0.2 (iv) Z 3 2 1 0 −1 P (Z) 0.3 0.2 0.4 0.1 0.05

Answer 1

For the probability distribution, sum of the probabilities of all events is equal to 1.

(i)

Sum of the probabilities P S is,

P S =0.4+0.4+0.2 =1

Thus, for the given random variable X is a probability distribution.

(ii)

The probability cannot be negative.

Thus, −0.1 is negative so that X is not a probability distribution.

(iii)

Sum of the probabilities P S is,

P S =0.6+0.1+0.2 =0.9 ≠1

Thus, it is clear that X is not a probability distribution.

(iv)

Sum of the probabilities P S is,

P S =0.3+0.2+0.4+0.1+0.05 =1.05 ≠1

Thus, it is clear that X is not a probability distribution.