Thread: Cumulative distribution function integration

The Question:
The continuous random variable X has probability density function given by:





a) Sketch the graph of f.
b) Explain why the value of n, the median of X, is 1.
c) Show that the value of u, the mean of X, is .
d) Find P(X < 3u - n).

I've done a), b), and c), but am stuck on d).

My Attempt:
F(x) (the cumulative distribution function for X) is
, which becomes:
with limits 1 and x.

Substituting:
.

Now 3u - n = .

Hence =:

.

This works out to .

However, the actual answer is , and the cumulative distribution function F(x) is .

Some advice on how to proceed would be appreciated.

isx99

Originally Posted by isx99

The Question:
The continuous random variable X has probability density function given by:





a) Sketch the graph of f.
b) Explain why the value of n, the median of X, is 1.
c) Show that the value of u, the mean of X, is .
d) Find P(X < 3u - n).

Now as the integral may be written:



CB

Thank you for your reply. This is a much simpler method than the one I was using, and it is also much easier to understand.

isx99