01:960:285 Lecture Notes - Lecture 2: Bayes Estimator, Sampling Distribution, Rivet

105 views3 pages
Rutgers University - Stat 285, Section 07 Spring 2017
Second MIDTERM March 30, 2017
BAYES Problem 1:
A total of 46 percent of the voters in a certain city classify themselves as Independents,
whereas 30 percent classify themselves as Liberals and 24 percent say that they are
Conservatives. In a recent local election, 35 percent of the Independents, 62
percent of the Liberals, and 58 percent of the Conservatives voted. A voter is chosen at
random. Given that this person voted in the local election, what is the probability that he
or she is an Independent? (15 points)
Solution Problem 1:
Let I, L, and C be the event that a random person is an independent, liberal, or a
conservative respectively. Let V be the event that a person voted. Then from the
problem we are given that
P(I) = 0.46 , P(L) = 0.3 , P(C) = 0.24
P(V |I) = 0.35 , P(V |L) = 0.62 , P(V |C) = 0.58 .
We want to compute P(I|V ), which by Baye’s rule is given by;
P(I|V ) =
We need to calculate P(V ) which we do (as above) by conditioning on the various types
of voters: P(V ) = P(V |I)P(I) + P(V |L)P(L) + P(V |C)P(C)
= 0.35(0.46) + 0.62(0.3) + 0.58(0.24) = 0.4862 .
Then the requested conditional probability is given by
P(I|V ) =
)46.0(35.0 =
Binomial Problem 2
An airline, having observed that 2% of the people making reservations fail to show up
for the flight, sells 100 tickets for a flight that has 98 seats. (That is, they assume that at
least 2 people will fail to show up for the flight.)
What is the probability that fewer than 2 people fail to show up for the flight? [Assume
that the people act independently, i.e., assume that each person shows upor does not
show upindependently of the behavior of the other people.] Give a mathematical
expression for the exact answer.
[Note: You do not necessarily have to compute an exact decimal number, but your final
answer should have only numbers in it (i.e. no parameters such as n, p or x) and use
only the operations of multiplication, addition and raising to a power.] (14 points)
Unlock document

This preview shows page 1 of the document.
Unlock all 3 pages and 3 million more documents.

Already have an account? Log in

Get OneClass Notes+

Unlimited access to class notes and textbook notes.

YearlyBest Value
75% OFF
$8 USD/m
$30 USD/m
You will be charged $96 USD upfront and auto renewed at the end of each cycle. You may cancel anytime under Payment Settings. For more information, see our Terms and Privacy.
Payments are encrypted using 256-bit SSL. Powered by Stripe.