# Probability

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

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)=

1. 👍 0
2. 👎 0
3. 👁 571
1. The line was supposed to be
fX(x)=c/x^3 if x≥1, 0,otherwise.

1. 👍 0
2. 👎 0
2. c = 2

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2. 👎 0
3. 1 c=2
2 ???
3 d*2

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2. 👎 0
4. 2. P(X≤U)= 0.25

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2. 👎 0

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