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# Finding the median using the PDF watch

1. For a continuous random variable X, the Probability density function of X is:

1/4 if 0≤x≤1

3/4 if 1<x≤2

0 otherwise.

I'd like to know how to find the median of this distribution without actually sketching it or finding the CDF first (since I know how to do it using that way)?

Apparently the median = 4/3.

2. (Original post by zomgleh)
For a continuous random variable X, the Probability density function of X is:

1/4 if 0≤x≤1

3/4 if 1<x≤2

0 otherwise.

I'd like to know how to find the median of this distribution without actually sketching it or finding the CDF first (since I know how to do it using that way)?

Apparently the median = 4/3.

What's the definition of the median? How do you get the CDF from the density function? Can you see where to go from there?

(You don't have to find the exact cdf, but if you can easily, as you can in this case, why on earth wouldn't you want to use that method?)

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Updated: April 10, 2013
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