Homework Assignments
Homework 4

Suppose
.
 Show that and .
 Show that .
 Suppose and write . Show that .

Suppose you have a random number generator which is capable of
generating random numbers distributed as
.
Describe how to generate random vectors
.

Suppose
and
are r.v.s. Show that
is
minimized over all functions
when
is the function

Let
.
Let
, where

Suppose
where
 The value is measured. Determine the best estimate for .
 In a separate problem, the values and are measured. Determine the best estimate of .
 Determine a random vector which is a whitened version of .
 Ex 3.7.5. What is requested is , i.e., the mean subsequent lifetime given that the machine is still running after days. Then use the hint from the book. Note that in (a), .
 Ex 3.7.7. Hint: Show that robot faulty fault not detected . Hence argue that the number of faulty passed robots, given , is distributed as , which has mean . Hence show that .
 Ex 4.1.1(a)
 Ex 4.1.2
 Ex 4.2.1. Hint: think geometric r.v.
 Ex 4.2.2. Hint: max .
 Ex 4.4.1. Hint: integrate by parts.
 Ex 4.6.4(b)
Copyright 2008,
Todd Moon.
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.
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