Question: A density function is proportional to f(x) = x 3 (1 x) 7 , for 0 < x < 1. (a) Find the constant

A density function is proportional to f(x) = x³(1 − x)⁷, for 0 < x < 1.
(a) Find the constant of proportionality.
(b) Find the mean and variance of the distribution.
(c) Use R to find P(X > 0.5).

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