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6. A continuous random variable X has probability density function f(x) = 0 if x< 0...

6. A continuous random variable X has probability density function

f(x) =

0 if x< 0

x/4 if 0 < or = x< 2

1/2 if 2 < or = x< 3

0 if x> or = 3

(a) Find P(X<1)

(b) Find P(X<2.5)

(c) Find the cumulative distribution function F(x) = P(X< or = x). Be sure to define the function for all real numbers x. (Hint: The cdf will involve four pieces, depending on an interval/range for x.

(d) Find the expected value of X

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