Online EE 131A
Homework #4
Fall 2010
Due Oct. 27th
K. Yao
Read LeonGarcia (3rd edition), pp. 146152; 163180
1. An air defense system consists of n independent radar sets over a given area. Assume
each radar has a probability of 0
.
9 of detecting an airplane. The system declares an
airplane is present if one or more of the radar detects an airplane. Find the probability
the system will declare an airplane if (a)
n
= 2, (b)
n
= 4. (Hint: Let
X
= number of
radar sets out of n that detects an airplane. What is the distribution of
X
?) (c) How
large must
n
be in order for the system to declare an airplane with a 0
.
999 probability?
2. In 1985 the median income of a family in the U.S. was $27
,
735 (i.e., onehalf of the
families has less than that income and onehalf has more than that income). Among
four randomly selected families, ﬁnd the probability that (a) all four had incomes above
$27
,
735, (b) one of the four had an income less than $27
,
735.
3. Of all the toasters produced by a company, 60% are good, 30% are fair, 7% burn the
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 Fall '10
 KungYao
 Information Theory, Probability, Error detection and correction, K. Yao

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