1. The pdf of Y is f(y) = k(y^3) I[2,3](y) where k is a constant, real…

1. The pdf of Y is f(y) = k(y^3) I[2,3](y) where k is a
constant, real number.
(a) (5 points) Calculate the value of k so that f(y) is a valid
pdf.
(b) (5 points) Find E(Y ). Hint: write k as a fraction so you
don’t have to round until the end.
(c) (5 points) Find the 50th percentile of Y .
(d) (2 points) Briefly (1-2 sentences) explain why your answers
to parts (b) and (c) make sense.