The random variable 𝑋 has range [0,1] and pdf 𝑓(𝑥) = 𝑐𝑥2.
(a) Find 𝑐.

(b) Find the mean, variance and standard deviation of 𝑋.

(c) Find the median value of 𝑋.

(d) Suppose 𝑋1, … 𝑋16 are independent identically-distributed copies of 𝑋. Let 𝑋 be their average. What is the standard deviation of 𝑋?

(e) Suppose 𝑌 = 𝑋4. Compute 𝐸[𝑌 ]

(f) Find the pdf of 𝑌 .