Class Problems: Computing Expectations (discrete)
1. Compute the expected value of a binomial random variable with paramaters
n
and
p
by writing it down as a sum of
n
Bernoulli random variables.
2. The following problem was posed and solved in the 18th century by Daniel Bernoulli.
Suppose that a jar contains 2
N
cards, two of them marked 1, two marked 2, two
marked 3, and so on. Draw out
m
cards at random. What is the expected number of
pairs that still remain in the jar? (Interestingly enough, Bernoulli proposed the above
as a possible probabilistic model for determining the number of marriages that remain
intact when there are a total of
m
deaths among
N
married couples.)
3. A group of
N
people throw hats into the center of a room. The hats are mixed up,
and each person randomly selects one. Find the expected number of people that select
their own hats.
4. If
n
balls are randomly selected from an urn containing
N
balls of which
m
are white,
find the expected number of white balls selected.
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 Spring '08
 Klutke
 Probability theory, $1, 5 minutes, 10 minutes, $0.50, 2 minutes

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