Question

Verify whether the following function can be regarded as p.m.f. of the random variable X: 

\[ P(X) = \begin{cases} \frac{x - 1}3 & \quad \text{x } = \text{ 1,2,3}\\ 0 & \quad \text{} , \text{otherwise} \end{cases} \] 

Answer 1

Probability mass function is given as 

P(X) = `("x" - 1)/3`

Put x= 1, 2, 3 respectively, we will get the 

Probability distribution

X	1	2	3
P (X = x)	0	`1/3`	`2/3`

Each P(x) ≥ 0 

∑ P(x) = P(1) +P(2) +P(3) 

`= 0 +1/3 + 2/3 = 1`

∵ Given probability distribution function is p.m.f.