Question

The probability distribution of a random variable X is:

X	0	1	2	3	4
P(X)	0.1	k	2k	k	0.1

where k is some unknown constant.

The probability that the random variable X takes the value 2 is ______.

Options

• `1/5`

• `2/5`

• `4/5`

• 1

Answer 1

The probability that the random variable X takes the value 2 is `underlinebb(2/5)`.

Explanation:

We have 

P(0) + P(1) + P(2) + P(3) + P(4) = 1

0.1 + k + 2k + k + 0.1 = 1

0.2 + 4k = 1

4k = 0.8

k = 0.2 = `1/5`

Given P(2) = 2k

`= 2xx1/5 = 2/5`