The question is from a past paper with no solutions, so I am trying to complete them and confirm with you guys if this is correct.
a) Finding k, I solved for
for which I get
b) the CDF, I just took the integrals of all the terms so it should look like
c) Expected value of X
I want to confirm this before calculating the variance, because I am getting a negative mean of
I am attempting to calculate it as follows:
e) Find the probability that
It is greater than 0 if it is between [0,1], so I've taken the integral:
Apologies the question is long, but they are related.