The probability distribution function of a discrete random variable X

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»

(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