Let X be a continuous random variable with pdf: f(x) = ax^2 - 2ax, 0 =< x =<2 a)

ID: 3389331 • Letter: L

Question

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..

Let X be a continuous random variable with pdf: f(x) = ax^2 - 2ax, 0 =< x =

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