Which of the following represent discrete probability distri

Which of the following represent discrete probability distributions? If any are not, explain why they are not.

x

p(x)

-1

0.30

1/2

0.15

2

0.40

4 1/4

0.15

Solution

Here all the 3 distributions are discrete distributions.

Discrete random variable is defined as a random variable which takes a countable number of values.

For first distribution P(x)>0 for x={-1,1/2,2,41/4} which is countable.

For second distribution P(x)>0 for x={0,1,2,3} which is countable.

for third distribution P(x)>0 for x={0,1,2,3,4} which is countable.

In all the three cases sum(P(x)) = 1.

Hence all the three distributions given are discrete.