Consider the probability density function f (x) = Ax3
Chapter 4, Problem 4.5.1(choose chapter or problem)
Consider the probability density function f (x) = Ax3 (1x)2 for 0 x 1 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.
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