# Random Variables

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Suppose X1 and X2 are independent exponential (λ) random variables. Let Y1=X1-X2 and Y2=X2.

a) Find the joint density of Y1 and Y2.

b) Find the marginal density of Y1.

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##### Solution Summary

Suppose X1 and X2 are independent exponential (λ) random variables. Let Y1=X1-X2 and Y2=X2.

a) Find the joint density of Y1 and Y2.

b) Find the marginal density of Y1.

##### Solution Preview

because,

p(X1,X2) = p(X1)*p(X2) = l^2*exp(-l(X1+X2))

raed l as lembda.

del(Y1)/del(X1) = 1

del(Y1)/del(X2) = -1

del(Y2)/del(X1) = 0

del(Y2)/del(X2) = ...

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- BEng, Allahabad University, India
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