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)=