Question: Consider the density function of a real random variable X. fX(x) = c(1 x^2 ), if 1 < x < 1, 0, otherwise, where the

Consider the density function of a real random variable X.

fX(x) = c(1 x^2 ), if 1 < x < 1,

0, otherwise,

where the constant c R

a) Find c so fX() is a probability density function.

b) Compute the mean and variance of X.

c) Define Y = X^3 . Compute P(Y > (1/27)).

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