Answer to Question #127610 in Statistics and Probability for Harsha

Question

A discrete random variable X has the following probability distribution:

x - 1, 2, 3, 4
P(X=x) - 1/3, 1/3, k, 1/4

Where k is a constant.
(a) Find the value of k.
(b) Find P(X ≤3).

Answer 1

Solution:

(a)

The sum of all probability is 1.

So,

P(X=1)+P(X=2)+P(X=3)+P(X=4)=1.

1/3+1/3+k+1/4=1.

11/12+k=1.

k=1/12.

P(X=3)=1/12.

(b) P(X≤3)= P(X=1)+P(X=2)+P(X=3)

P(X≤3)=1/3+1/3+1/12

P(X≤3)=3/4