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 distribution (c) What are the parameter values a and b of a beta distribution for which this is the probability density function Check your answers to part (b) using the general formulas for beta distributions

Question: Consider the probability density function f(x) = Ax3 (I - x)2 for 0 < x < I and f(x) = 0 elsewhere. (a) Find the

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.

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