Find the median of the random variable with the probability density function given below. (Round your answer to four decimal places.)

$$f(x) = 0.06\, e^{−0.06\,x}\text{ on }[0, +\infty)$$

Any help solving this problem would be greatly appreciated as I am extremely confused on where to even start.


closed as off-topic by Did, user251257, Namaste, Shailesh, JonMark Perry Nov 22 '16 at 5:21

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, user251257, Namaste, Shailesh, JonMark Perry
If this question can be reworded to fit the rules in the help center, please edit the question.

  • 4
    $\begingroup$ Hint: the median is the value $m$ such that $P(x≤m)=\frac 12$ So, just compute $P(x≤m)$ for variable $m$ and solve for $m$ $\endgroup$ – lulu Nov 21 '16 at 22:10
  • 2
    $\begingroup$ You may want to have a look a exponential distributions. $\endgroup$ – A.G. Nov 21 '16 at 22:13
  • 1
    $\begingroup$ You can also search this site with keywords "median distribution random variable"... $\endgroup$ – A.G. Nov 21 '16 at 22:15

The median is located where the $\text{cdf}$ reaches $1/2$.


$$\text{cdf}(x)=\int_0^x\text{pdf}(x) dx=\int_0^x0.06e^{-0.06x}dx=-\left.e^{-0.06x}\right|_0^x=\frac12.$$

I let you the conclude.

  • $\begingroup$ Is the answer then .5309? $\endgroup$ – user344249 Nov 21 '16 at 22:19
  • 1
    $\begingroup$ Probably not. How do you get this value ? $\endgroup$ – Yves Daoust Nov 21 '16 at 22:20
  • $\begingroup$ Wait I did it wrong, I should have actually done ln(.5)/(-.06) and that would then give me the answer of 11.5525 which is correct $\endgroup$ – user344249 Nov 21 '16 at 22:23
  • $\begingroup$ Thank you so much for your help $\endgroup$ – user344249 Nov 21 '16 at 22:23

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