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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) Findingk, I solved for

for which I get

b) the CDF, I just took the integrals of all the terms so it should look like

0 if

if

if

0 if

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.