The continuous random variable X has probability density function f given by
f(x) =
, for
f(x) = 0, otherwise.
a] Evaluate E
.
b] Find an expression for the cumulative distribution function.
c] Evaluate P(X
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! .
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