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

Question

fX(x)=⎧⎩⎨cx3 if x≥1, 0,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=

P(X≤U)=

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

For 0≤d≤1, fD(d)=

Answer 1

The line was supposed to be
fX(x)=c/x^3 if x≥1, 0,otherwise.

Answer 2

c = 2

Answer 3

1 c=2
2 ???
3 d*2

Answer 4

2. P(X≤U)= 0.25