# The probability distribution of a discrete random variable X is - Mathematics and Statistics

Sum

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)

#### Solution

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

Concept: Probability Distribution of a Discrete Random Variable
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