The continuous random variable X has probability density function f given by

f(x) = $\displaystyle \frac{6}{5}x (x - 1)$, for $\displaystyle 1 \leq x \leq 2$

f(x) = 0, otherwise.

a] Evaluate E$\displaystyle \frac{1}{X}$.

b] Find an expression for the cumulative distribution function.

c] Evaluate P(X $\displaystyle \leq$ 1.75).

d] State, with a reason, whether the median of X is greater or less than 1.75.

For part a] I calculated E(X) which I found to be

, so E(1/X) was done by

which is 10/17, or 0.58 or something like that. Is this right?

Mr F says: **No!** $\displaystyle {\color{red} E \left( \frac{1}{X} \right) \neq \frac{1}{E(X)}}$.
For part b] I had

.

Mr F says: Wrong. If this was correct then it should equal 1 when x = 2. It doesn't.
For c] if P(X

1.75) is F(1.75), then that should be 0.30625 if part b] is correct,

and to answer d] you can say that the median of X must be greater than 0.5 because the value of 1.75 is not greater than 0.5.

Am I right or did something go wrong?

Thanks for any help