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1. Suppose a random variable X has a probability density function f(x)= {cx^2 -1<x<1, {0 otherwise...

1. Suppose a random variable X has a probability density function

f(x)= {cx^2 -1<x<1,

{0 otherwise

where c > 0.

(a) Determine c.
(b) Find the cdf F ().
(c) Compute P (-0.5 < X < 0.75).
(d) Compute P (|X| > 0.25).
(e) Compute P (X > 0.75 | X > 0).
(f) Compute P (|X| > 0.75| |X| > 0.5).

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