18.05 Problem Set 9, Spring 2014
Problem 1. (10 pts.) Condent coin.
Recall the condent coin from pset 7. It was spun on its edge 250 times and came up
heads 140 times. Our null hypothesis was that the
18.05 Problem Set 8, Spring 2014
Problem 1. (10 pts.) Jerry steals a JP Licks token and asks Jon to perform a test
at signicance level = 0.05 to investigate whether the coin is fair or biased toward
t
18.440 Midterm 2, Spring 2014: 50 minutes, 100 points
1. (20 points) Consider a sequence of independent tosses of a coin that is
biased so that it comes up heads with probability 3/4 and tails with
pr
18.440 Midterm 2, Fall 2012: 50 minutes, 100 points
1. (10 points) Suppose that a fair die is rolled 18000 times. Each roll turns
up a uniformly random member of the set cfw_1, 2, 3, 4, 5, 6 and the r
18.05 Problem Set 7, Spring 2014 Solutions
Problem 1. (10 pts.) (a) H0 : = 0.5
HA : one-sided > 0.5, two-sided = 0.5.
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Test statistic: x = number of heads in 250 spins.
Data: x = 140.
One-sided data
18.05 Problem Set 8, Spring 2014 Solutions
Problem 1. (10 pts.) (a) Let x = number of heads
Model: x binomial(12, ).
Null distribution binomial(12, 0.5).
Data: 3 heads in 12 tosses.
Since HA is one-si
18.05 Problem Set 7, Spring 2014
Problem 1. (10 pts.)
Condent coin: III (Quote taken from Information
Theory, Inference, and Learning Algorithms by David J. C. Mackay.)
A statistical statement appeare
18.05 Problem Set 9, Spring 2014 Solutions
Problem 1. (10 pts.) (a) We have x binomial(n, ), so E(X) = n and
Var(X) = n(1 ). The rule-of-thumb variance is just n . So the distributions being
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plotted
18.05 Problem Set 6, Spring 2014
Problem 1. (10 pts.) Beta try again. (Adapted from Information Theory, Inference, and Learning Algorithms by David J. C. Mackay.)
A statistical statement appeared in T
18.05 Final Exam Solutions
Part I: Concept questions (58 points)
These questions are all multiple choice or short answer. You dont have to show any work.
Work through them quickly. Each answer is wort
18.05 Problem Set 6, Spring 2014 Solutions
Problem 1. (10 pts.) (a) Throughout this problem we will let x be the data of
140 heads out of 250 tosses. We have 140/250 = .56. Computing the likelihoods:
18.05 Final Exam
2
Part I: Concept questions (58 points)
These questions are all multiple choice or short answer. You dont have to show any work.
Work through them quickly. Each answer is worth 2 poin
Practice Final
This exam is closed book, no books, papers or recording devices permitted. You may use theorems
from class, or the book, provided you can recall them correctly.
Problem 1
Suppose
an