Consider the probability density function f(x) = Ax3 (I - x)2 for 0 < x < I

Question:

Consider the probability density function
f(x) = Ax3 (I - x)2
for 0 < x < I and f(x) = 0 elsewhere.
(a) Find the value of A by direct integration.
(b) Find by direct integration the expectation and variance of this What are the parameter values a and b of a beta for which this is the probability density function? Check your answers to part (b) using the general formulas for beta distributions.
Distribution
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