Question

The probability distribution of a discrete random variable X is:

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

find P(X≤4)

Answer 1

Given X is discreate r . v.

∴ P(x) is p.m.f.

p.m.f = ∑ pi = 1

i.e. k + 2k + 3k + 4k + 5k = 1

i.e. 15 k = 1

i.e. k = `1/15`

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

= k + 2k + 3k + 4k

= 10k

=`10 xx 1/15`

= `2/3`