# Combinations and probability: probability density function

The probability density function of $X$, the lifetime of a certain type of electronic device (measured in hours), is given by $f(x)=xe^{-x}$ for $x\in[0,\infty)$. Find $P(X>2)$.

Please advise me how to find $P(X > 2)$, I really have no idea.

## 1 Answer

This looks like a homework question. If so, I would strongly suggest you go to your TA or prof. office hours and have them help you understand this. This is a very core idea in intro stats, and you will have lots of problems going forward if you don't tackle this first.

That being said, $P(X>2) = 1- P(X\leq2) = 1- F(2) = \int_0^2 f(x) dx$ You have to integrate a probability density to get a probability, just like you integrate a concentration over a volume to get a mass. Here, you want the probability contained on [0,2]. With continuous variables, any question involving probabilities will, at least conceptually, require integrating the density (unless there is a trick/shortcut for a particular problem).

Study hard :)...hope that helps. Please talk with your prof. though and make sure you get the basics of pdf vs cdf, density vs. probabilty down so you can have a smoother rest of the course.