EE 351K PROBABILITY & RANDOM PROCESSES
FALL 2011
Instructor: Sujay Sanghavi
[email protected]
Homework 10
Due: December 5th @ ENS 428
Focus: Classical Statistical Inference (Chapter 9 in Textbook)
Problem 1
A radar works by transmitting a pulse, and seeing if there is an echo. Ideally, an echo means object is
present, and no echo means no object. However, some echoes might get lost, and others may be generated
due to other surfaces. To improve accuracy, a radar transmits
n
pulses, where
n
is a fixed number, and sees
how many echoes it gets. It then makes a decision based on this number.
Let
p
1
be the probability of an echo for a single pulse when there is no object, and
p
2
be the probability
when there is an object. Assume
p
1
< p
2
. What is the maxlikelihood estimation rule for whether the object
is present or absent?
Problem 2
A source emits a random number of photons
K
each time that it is triggered. We assume that the PMF of
K
is
p
K
(
k
;
θ
) =
c
(
θ
)
e

θk
,
k
= 0
,
1
,
2
,
. . . .
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 Spring '07
 BARD
 Probability theory, WI, ML estimator, EE 351K Probability, Classical Statistical Inference

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