ST501 Fundamentals of Inference – Summer 2015
Homework #4 – due Friday, 17 July
Do all of the following exercises, but only turn in those with an
asterisk (*) – there are four.
From Chapter 2
• 2.39 also find F −1 (u)
• 2.44
• 2.52 * AND answer same questions with µ = 67 and σ = 4
• 2.69
From Chapter 3
• 3.1
• 3.8
• 3.12
• 3.14 *
• 3.19
Other problems:
1. Let the random variable U have the uniform(0,1) distribution. Show that
Y = − log(U ) has the exponential distribution.
3(1 − x)2 0 < x < 1
2. * Let X have the pdf
What is the pdf of Y =
0
otherwise
(1 − X)3 ? Be sure to state the support of Y .
3. * Suppose (X,Y) has the joint pdf
−y
e
fX,Y (x, y) =
0
0<x<y<∞
otherwise
(a) Are X and Y independent? Explain.
(b) Find the marginal pdf of Y , giving the name for this distribution and
specifying its parameters.
(c) Find P r(X + Y < 3)
1