Question

Given below is the probability distribution of a discrete random variable x.

X	1	2	3	4	5	6
P(X = x)	K	0	2K	5K	K	3K

Find K and hence find P(2 ≤ x ≤ 3)

Answer 1

We have `sumP(X = x)` = 1

∴ K + 0 + 2K + 5K + K + 3K = 1

∴ 12K = 1,

∴ K = `1/12`

Hence the probability distribution is

X	1	2	3	4	5	6
P(X = x)	`1/12`	0	`2/12`	`5/12`	`1/12`	`3/12`

∴ P(2 ≤ x ≤ 3) = P(x = 2) + P(x = 3)

= `0 + 2/12`

= `1/6`