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# Random Variables

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Suppose X1 and X2 are independent exponential (&#955;) 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 Summary

Suppose X1 and X2 are independent exponential (&#955;) 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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• MSc , Pune University, India
• PhD (IP), Pune University, India
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