Finding the median given a p.d.f.

Intsecxtanx · #1 $Old$ November 3rd, 2009, 02:24 PM

Let X have the p.d.f. f (x) = c * e^(Abs(x)) for -1<= x < 1 (please note the absolute value marks.

I determined c to be 1/(2e-2)
but how do you calculate the median of X. I believe it has something to do with the 50th percentile but I'm not sure how to make that calculation.

Thank you for your time.

pickslides · #2 $Old$ November 3rd, 2009, 02:56 PM

Quote:

Originally Posted by Intsecxtanx $View Post$

Let X have the p.d.f. f (x) = c * e^(Abs(x)) for -1<= x < 1 (please note the absolute value marks.

I determined c to be 1/(2e-2)
but how do you calculate the median of X. I believe it has something to do with the 50th percentile but I'm not sure how to make that calculation.

Thank you for your time.

First find c by

$\int_{-1}^1 c\times e^{|x|}~dx = 1$

Then once you have c

find a such that $\int_{a}^1 c\times e^{|x|}~dx = 0.5$

matheagle · #3 $Old$ November 3rd, 2009, 04:20 PM

This is a symmetric distribution about 0, so 0 better be the median.