Let X be a continuous random variable with pdf fx ax2 2ax

Let X be a continuous random variable with pdf:

f(x) = ax^2 - 2ax, 0 =< x =<2

a) What should \"a\" be in order for this to be a legitmate p.d.f?

b) What is the distribution funtion (c.d.f) for X?

c) What is Pr(0 =< X < 1)? Pr( X > 0.5)? Pr(X>3)?

d) What is the 90th percentile value of this distribution? (It will end up with a cubic equation that you need to solve and solve it numerically)

e) What are the mean and variance of this distribution?

I don\'t get only this question so please provide all the solutions..

Solution