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Let X have a uniform distribution on the interval (7, 13). Find the probability that the...

Let X have a uniform distribution on the interval (7, 13). Find the probability that the sum of 2 independent observations of X is greater than 25.

Expert Solution

Ley Y and Z be two independent observations from X~U(7,13)

SO,

, 7<x<13

Define, , 0<P<1

So,

pdf of P,

P ~ Uniform (0,1)

Thus,

independently

By Method of convolution, pdf of ,

if 1<t<2 ,

So,

if 0<t<1 ,

We have to find P(X+Y>25) :

milcah answered 3 months ago

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