# Finding probability given joint pdf.

1. Nov 25, 2009

1. The problem statement, all variables and given/known data

Let X1 X2 X3 be independent and identically distributed random variables with common pdf f(x) = e^-x 0<x<infinity, zero elsewhere.

Evaluate P(X1 < X2|X1 < 2X2) and P(X1 < X2 < X3|X3 < 1).

3. The attempt at a solution

Would appreciate any hints as to where to start...

2. Nov 25, 2009

### clamtrox

I haven't actually studied any statistics so there might be an easier way of doing this but this is how I'd do it...

Having a conditional probability means that you essentially have a 100% probability for the condition, that is

$$\int_{x_1 < 2x_2} dx_1 dx_2 f(x_1, x_2) = 1$$

This gives you the probability density given the condition that x_1 < 2 x_2. You can then use that to find the probability that x_1 < x_2.

3. Nov 25, 2009