Post Exam 2 Practice Questions, 18.05,
Spring 2014
Jeremy Orlo and Jonathan Bloom
Note: This is a set of practice problems for the material that came after exam 2. In
preparing for the nal you should use the previous review materials, the psets, the
notes
Conjugate priors: Beta and normal
Class 15, 18.05, Spring 2014
Jeremy Orlo and Jonathan Bloom
1
Learning Goals
1. Understand the benets of conjugate priors.
2. Be able to update a Beta prior given a Bernoulli, binomial, or geometric likelihood.
3. Underst
Continuous Data with Continuous Priors
Class 14, 18.05, Spring 2014
Jeremy Orlo and Jonathan Bloom
1
Learning Goals
1. Be able to construct a Bayesian update table for continuous hypotheses and continuous
data.
2. Be able to recognize the pdf of a normal
Name
18.05 Final Exam
No calculators.
Number of problems
16 concept questions, 16 problems, 21 pages
Extra paper
If you need more space we will provide some blank paper. Indicate clearly
that your solution is continued on a separate page and write your na
The Frequentist School of Statistics
Class 17, 18.05, Spring 2014
Jeremy Orlo and Jonathan Bloom
1
Learning Goals
1. Be able to explain the dierence between the frequentist and Bayesian approaches to
statistics.
2. Know our working denition of a statistic
Choosing priors
Class 15, 18.05, Spring 2014
Jeremy Orlo and Jonathan Bloom
1
Learning Goals
1. Learn that the choice of prior aects the posterior.
2. See that too rigid a prior can make it dicult to learn from the data.
3. See that more data lessons the
Condence Intervals for the Mean of Non-normal Data
Class 23, 18.05, Spring 2014
Jeremy Orlo and Jonathan Bloom
1
Learning Goals
1. Be able to derive the formula for conservative normal condence intervals for the
proportion p in Bernoulli data.
2. Be able
Null Hypothesis Signicance Testing I
Class 17, 18.05, Spring 2014
Jeremy Orlo and Jonathan Bloom
1
Learning Goals
1. Know the denitions of the signicance testing terms: NHST, null hypothesis, alternative
hypothesis, simple hypothesis, composite hypothesis
Condence Intervals: Three Views
Class 23, 18.05, Spring 2014
Jeremy Orlo and Jonathan Bloom
1
Learning Goals
1. Be able to produce z, t and 2 condence intervals based on the corresponding stan
dardized statistics.
2. Be able to use a hypothesis test to co
Bayesian Updating with Continuous Priors
Class 13, 18.05, Spring 2014
Jeremy Orlo and Jonathan Bloom
1
Learning Goals
1. Understand a parameterized family of distributions as representing a continuous range
of hypotheses for the observed data.
2. Be able
Beta Distributions
Class 14, 18.05, Spring 2014
Jeremy Orlo and Jonathan Bloom
1
Learning Goals
1. Be familiar with the 2-parameter family of beta distributions and its normalization.
2. Be able to update a beta prior to a beta posterior in the case of a
Exam 1 Practice Questions II, 18.05, Spring 2014
Note: This is a set of practice problems for exam 1. The actual exam will be much
shorter.
1. A full house in poker is a hand where three cards share one rank and two cards
share another rank. How many ways
Introduction to Statistics
Class 10, 18.05, Spring 2014
Jeremy Orlo and Jonathan Bloom
1
Learning Goals
1. Know the three overlapping phases of statistical practice.
2. Know what is meant by the term statistic.
2
Introduction to statistics
Statistics deal
Linear regression
Class 25, 18.05, Spring 2014
Jeremy Orlo and Jonathan Bloom
1
Learning Goals
1. Be able to use the method of least squares to t a line to bivariate data.
2. Be able to give a formula for the total squared error when tting any type of cur
Bayesian Updating: Probabilistic Prediction
Class 12, 18.05, Spring 2014
Jeremy Orlo and Jonathan Bloom
1
Learning Goals
1. Be able to use the law of total probability to compute prior and posterior predictive
probabilities.
2
Introduction
In the previous
Bayesian Updating: Odds
Class 12, 18.05, Spring 2014
Jeremy Orlo and Jonathan Bloom
1
Learning Goals
1. Be able to convert between odds and probability.
2. Be able to update prior odds to posterior odds using Bayes factors.
3. Understand how Bayes factors
Notational conventions
Class 13, 18.05, Spring 2014
Jeremy Orlo and Jonathan Bloom
1
Learning Goals
1. Be able to work with the various notations and terms we use to describe probabilities
and likelihood.
2
Notation and terminology for data and hypotheses
Exam 2 Practice Questions, 18.05, Spring 2014
Note: This is a set of practice problems for exam 2. The actual exam will be much
shorter. Within each section weve arranged the problems roughly in order of di
culty.
1
Topics
Statistics: data, MLE (pset 5)
Maximum Likelihood Estimates
Class 10, 18.05, Spring 2014
Jeremy Orlo and Jonathan Bloom
1
Learning Goals
1. Be able to dene the likelihood function for a parametric model given data.
2. Be able to compute the maximum likelihood estimate of unknown parame
Exam 1 Practice Questions I, 18.05, Spring 2014
Note: This is a set of practice problems for exam 1. The actual exam will be much
shorter.
1. There are 3 arrangements of the word DAD, namely DAD, ADD, and DDA. How
many arrangements are there of the word P
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-sided the rejection region is one-sided. Since HA says th
Exam 1 Practice Questions I solutions, 18.05,
Spring 2014
Note: This is a set of practice problems for exam 1. The actual exam will be much
shorter.
1.
Sort the letters: A BB II L O P R T Y. There are 11 letters in all. We build
arrangements by starting w
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 worth 2 points.
Concept 1.
answer: C. (i) and (ii)
Concept
Practice Exam 1: Long List
18.05, Spring 2014
1
Counting and Probability
1. A full house in poker is a hand where three cards share one rank and two cards
share another rank. How many ways are there to get a full-house? What is the
probability of getting
Exam 1 Practice Questions II solutions, 18.05,
Spring 2014
Note: This is a set of practice problems for exam 1. The actual exam will be much
shorter.
1.
We build a full-house in stages and count the number of ways to make each
stage:
13
Stage 1. Choose th
Post Exam 2 Practice Questions solutions, 18.05,
Spring 2014
Jeremy Orlo and Jonathan Bloom
1
Condence intervals
To practice for the exam use the t and z-tables supplied at the end of this le. Be
sure to learn to use these tables. Note the t and z-tables
Exam 1 Practice Exam 1: Long List solutions,
18.05, Spring 2014
1
Counting and Probability
1.
We build a full-house in stages and count the number of ways to make each
stage:
13
Stage 1. Choose the rank of the pair:
.
1
4
Stage 2. Choose the pair from tha
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
4
plotted are
binomial(250, ), N(250, 250(1 ), N(250, 250/4).
No