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Let Y be a random variable with pdf fY (y) = − π/8 sin (πy), if...

Let Y be a random variable with pdf

fY (y) = − π/8 sin (πy), if − 1 ≤ y ≤ 0

c sin (πy), if 0 ≤ y ≤ 1

0, otherwise.

(a) What is c?

(b) What is Fy(y), the CDF of Y ?

(c) What is E[Y ]?

(d) What is P(Y > 0)?

(e) What is P(Y > 1/2|Y > 0)

Math   Statistics-And-Probability   
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