Question: 5.5 Functions of random variables 71 Exercise 5.48 Show that the density function f (x) = 1 x(1 x) if 0 <

5.5 Functions of random variables 71 Exercise 5.48 Show that the density function f (x) =



1

π√x(1 − x)

if 0 < x < 1, 0 otherwise, has distribution function with the form F(x) = c sin−1 √x if 0 < x < 1, and find the constant c.

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