Question

State the following are not the probability distributions of a random variable. Give reasons for your answer.

X	0	1	2	3	4
P(X)	0.1	0.5	0.2	-0.1	0.3

Answer 1

It is known that the sum of all the probabilities in a probability distribution is one.

It can be seen that for X = 3, P (X) = −0.1

It is known that probability of any observation is not negative. Therefore, the given table is not a probability distribution of random variables.