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# (Solved): Let Z be a random variable equal to the sum of two independent random variables X and Y : Z=X+Y Th ... Let be a random variable equal to the sum of two independent random variables and : The probability density functions of and are given by a) Find and . b) Find the probability density function of . c) What is the probability that .

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a) To find the values of a and b,
we need to ensure that the probability density functions (PDFs) of X and Y integrate to 1 over their respective support intervals.

Given:

To find a, we integrate   over its support interval   :

so   when   , and 0 otherwise, we have:

To find b, we integrate    over its support interval   :

Since u(y) = 1 when y ? 0, and 0 otherwise, we have:

Applying integration, we get:

b = 10

a is 1/10 and b value is 10.

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