Let X and Y be two independent random variables with X =d R(0, 2) and Y...

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Question

Let X and Y be two independent random variables with X =d R(0, 2) and Y...

Let X and Y be two independent random variables with X =d R(0, 2) and Y =d exp(1).

(a) Use the convolution formula to calculate the probability density function of W =X+Y.

(b) Derive the probability density function of U = XY .

math Statistics-And-Probability

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Answer 1

Answer #1

Here .

a)We find the PDF of using convolution.

Thus,

b) We Derive the probability density function of using the CDF method,

The distribution of is exponential.

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Answer 2

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