Statistics Question

Question

The life (in months) of a certain computer component has a probability density function defined by f(x)=14e−x/4 for x in [0,∞). Find the probability that a component randomly selected will last between 11 and 20 months?

Answer 1

Technically this isn't a valid probability density function because when you integrate f(x) from 0 to infinity you don't get 1. I think you made a typo and the probability density function should be f(x) = (1/4)e^(-x/4). doing the problem this way if you wanted the find the probability that a component will be between 11 and 20 months you just integrate f(x) from 11 to 20. I'm assuming x is measured in months. The antiderivative of f(x) is -e^-x/4. Evaluating this from 11 to 20 gives e^-11/4 - e^-5 = .057.

Hope this helps!