Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

The lifetime of a machine part has a continuous distribution on the interval (0, 40) with probability density function f, where f(x) is proportional to (10 + x)^(−2). Calculate the probability that the lifetime of the machine part is less than 6.

share|cite|improve this question
up vote 1 down vote accepted


You'll need your probability density function to have total integral 1:

$$ \int_0^{40}f(x)dx=1 $$ So, you'll have to find the right constant to stick in front of $(10+x)^{-2}$.

Then, to calculate the probability that the lifetime is less than 6, you simply integrate $f(x)$ from 0 to 6.

share|cite|improve this answer
Oh wow! So that was what proportional meant. Thanks! – John Chang Dec 12 '12 at 2:08
Yep, any time we say "$f(x)$ is proportional to $g(x)$" we just mean $f(x)=Cg(x)$ for some constant $C$. – icurays1 Dec 12 '12 at 2:10

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.