Question

Determine whether or not the table is a valid probability distribution of a discrete random variable. Explain fully.
a.

x	-2	0	2	4
P(x)	0.3	0.5	0.2	0.1

b.

x	0.5	0.25	0.25
P(x)	-0.4	0.6	0.8

c.

x	1.1	2.5	4.1	4.6	5.3
P(x)	0.16	0.14	0.11	0.27	0.22

Answer 1

In part a) we find that the probabilities sum up to 1 and are non negative. So it represents a valid probability distribution of a discrete random variable.

In part b) we find that the first value of P(x) is negative. Probability is a non negative quantity always and lies between 0& 1. So (b) cannot represent a probability distribution.

In part c) although the probabilities are non negative, they don't sum up to 1. For being a probability distribution of a random variable, the sum of the probabilities should be 1. Here the sum is 0.68. Hence, (c) also fails to be a valid probability distribution.