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Getting the cumulative distribution function for this continuous random variable.

I need to find the median for this random variable, X, and whilst I can sketch it easily and find it, I'd like to know how to do it using the cumulative distribution function.

The Probability density function of X:

1/4 if 0≤x≤1

3/4 if 1<x≤2

0 otherwise.

Apparently the median = 4/3.

Thanks in advance!

Reply 1

24DJF

To find the CDF, you'll need to integrate the first part of the PDF to find F[x] and add that onto the integral of the second part. Reply to me and I'll post a picture if you need to

Reply 2

ztibor

Original post by zomgleh

Using CDF you should to solve an inequality system for m

\displaystyle \int_{-\infty}^m dF(x) \ge \frac{1}{2}

\displaystyle \int_{m}^{\infty} dF(x) \ge \frac{1}{2}

The integrals are Riemann-Stieltjes integrals
More simple to calculate median from PDF

(edited 11 years ago)

Reply 3

zomgleh

Original post by 24DJF

To find the CDF, you'll need to integrate the first part of the PDF to find F[x] and add that onto the integral of the second part. Reply to me and I'll post a picture if you need to

Ok so I got the Cumulative distribution function to be--
0 for x<0

x/4 for 0≤x≤1

3x/4 - 1/2 for 1<x≤2

1 for x>2

But how do I know which one to choose in order to get the median?
F(m)=0.5 ?
Apparently it's the '3x/4 - 1/2 for 1<x≤2' one.