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Random Variables

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,
<br>p(X1,X2) = p(X1)*p(X2) = l^2*exp(-l(X1+X2))
<br>raed l as lembda.
<br>del(Y1)/del(X1) = 1
<br>del(Y1)/del(X2) = -1
<br>del(Y2)/del(X1) = 0
<br>del(Y2)/del(X2) = ...

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.

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