- #1

rayge

- 25

- 0

## Homework Statement

Let us choose at random a point from the interval (0,1) and let the random variable [itex]X_1[/itex] be equal to the number which corresponds to that point. Then choose a point at random from the interval (0,[itex]x_1[/itex]), where [itex]x_1[/itex] is the experimental value of [itex]X_1[/itex]; and let the random variable [itex]X_2[/itex] be equal to the number which corresponds to this point.

Compute [itex]P(X_1 + X_2 >= 1)[/itex]

## Homework Equations

The joint pdf is [itex]1/x_1 , 0<x_2<x_1<1[/itex]

## The Attempt at a Solution

Many. For one, set [itex]Y=X_1+X_2[/itex]. Then find [itex]P(Y>=1)[/itex]. Then evaluate [itex]\int_0^1\int_{1-x_2}^1 1/x_1 dx_1dx_2[/itex]. Evaluating this integral gives me zero.

The other solutions I come up with end up giving me [itex]ln(0)[/itex], which is undefined. Any suggestions on how to approach this?