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Find the value of C > 0 such that the function ?C sin2x, if0≤x≤π, f(x) =...

Find the value of C > 0 such that the function
?C sin2x, if0≤x≤π,
f(x) =
0, otherwise
is a probability density function.
Hint: Remember that sin2 x = 12 (1 − cos 2x).
2. Suppose that a continuous random variable X has probability density function given by the above f(x), where C > 0 is the value you computed in the previous exercise. Compute E(X).
Hint: Use integration by parts!
3. Compute E(cos(X)).
Hint: Use integration by substitution!

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