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

(i)P(0)+P(1)+P(2)=0.4+0.4+0.2=1
Therefore,it is a probability distribution of a random variable.
(ii)$P(3)=-0.1$which is not possible.
Therefore,it is not a probability distribution.
(iii$)P(-1)+P(0)+P(1)=0.6+0.1+0.2=0.9≠1$
Therefore,it is not a probability distribution.
(iv)$P(3)+P(2)+P(1)+P(0)+P(-1)=0.3+0.2+0.4+0.1+0.05=1.05≠1$
Therefore,it is not a probability distribution.