The probability distribution function of a discrete random variable X is f(x) = 2k, x = 1, f(x) = 3k, x = 3

Question

The probability distribution function of a discrete random variable X is 

\(f(x)=\begin{cases}2k,&x = 1\\ 3k,&x = 3\\ 4k,&x = 5\\ 0,& otherwise\end{cases}\)

where k is some constant.

Find (a) k and (b) P(X > 2).

Answer 1

(a) Given X is a discrete random variable. The probability distribution can be written as

X = x	1	3	5
P(x)	2k	3k	4k

We know that Σp(x) = 1 

⇒ 2k + 3k + 4k = 1 

⇒ 9k = 1 ⇒ k = 1/9 

(b) P(X > 2) = P(X = 3) + P(X = 5) 

= 3k + 4k 

= 7k

= 7/9