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)

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#### 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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