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## Homework Statement

Let [itex]X_1, X_2, X_3[/itex] be iid with common pdf [itex]f(x)=exp(-x)[/itex], [itex]0<x<infinity[/itex], [itex]0[/itex] elsewhere.

Evaluate [itex]P(X_1<X_2 | X_1<2X_2)[/itex]

## Homework Equations

[itex]f(X|Y) = f(x,y)/f(y)[/itex]

## The Attempt at a Solution

Since [itex]P(X_1<X_2)[/itex] is a subset of [itex]P(X_1<2X_2)[/itex], the intersection (edited, at first said union) should be [itex]P(X_1<X_2)[/itex], so the conditional should be [itex]P(X_1<X_2)/P(X_1<2X_2)[/itex] (edited). I evaluate this and get [itex](exp(-x_2) - 1 )/ (exp(-2x_2 ) - 1)[/itex], so I'm going wrong somewhere. Any suggestions welcome!

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