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).
F(x) (the cumulative distribution function for X) is
, which becomes:
with limits 1 and x.
Now 3u - n = .
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.