Question

Let X be a random variable that takes non-zero values in [1,∞), with a PDF of the form

fX(x)=⎧⎩⎨cx3,0,if x≥1,otherwise.


Let U be a uniform random variable on [0,2]. Assume that X and U are independent.

What is the value of the constant c?

c=

- unanswered

P(X≤U)=

- unanswered

Find the PDF of D=1/X. Express your answer in terms of d using standard notation .

For 0≤d≤1, fD(d)=