Homework 4, due on Apr 23, 2010
3.3.9
Out of
n
individual voters at an election,
r
vote Republican and
n
‐
r
vote Democrat. At the next election
the probability of a Republican switching to vote Democrat is
, and of a Democrat switching is
.
Suppose individuals behave independently. Find a) the expectation and b) the variance of the number of
Republican votes at the second election.
ଵ
ଶ
ଶ
ܦ
ଶ
ത
ଵ
ܦ
ଵ
ܦ
a)
Predict the value of
ܺ
ത
for large
n
.
000 the chance that your prediction is off by more than
߳
is
ely the least value of
n
such that your prediction of
ܺ
ത
is correct to within 0.01
3.4.18
3.3.12
A random variable
X
has expectation 10 and standard deviation 5.
a)
Find the smallest upper bound you can for
P
(
X
20
).
b)
Could
X
be a binomial random variable?
3.3.14
Suppose the average family income in an area is $10,000.
a)
Find an upper bound for the percentage of families with incomes over $50,000.
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 Spring '08
 ROSS
 Probability, Variance, Probability theory, upper bound, binomial random variable, nr vote Democrat

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