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## Homework Statement

Homework about a result in probability theory, but I don't understand one of the steps:

Let f(x) be the PDF of a continuous R.V which takes only non-negative values.

Why is the following true?

[itex]\int^{\infty}_0\int^{\infty}_xf(t) \mathrm{d}t \mathrm{d}x[/itex] =

[itex]\int^{\infty}_0\int^{t}_0f(t)\mathrm{d}x\mathrm{d}t[/itex]

## Homework Equations

N/A

## The Attempt at a Solution

We can change the order of integration but I only come up with:

[itex]\int^{\infty}_0\int^{\infty}_xf(t)\mathrm {d}t\mathrm {d}x[/itex] = [itex]\int^{\infty}_x\int^{\infty}_of(t)\mathrm {d}x\mathrm {d}t[/itex] =