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
Spring 2014 18.440 Final Exam Solutions
1. (10 points) Let X be a uniformly distributed random variable on [ 1, 1].
(a) Compute the variance of X 2 . ANSWER:
Var(X 2 ) = E[(X 2 )2 ]
and
E[X 2 ] =
2 2
Z
1
(x2 /2)dx =
1
4
E[(X ) ] = E[X ] =
so Var(X 2 ) = E
18.05 Exam 2 Solutions
Problem 1. (10 pts: 4,2,2,2) Concept questions
(a) Yes and yes. Frequentist statistics dont give the probability an hypothesis is true.
(b) True. Bayesian updating involves multiplying the likelihood and the prior. If the prior
is 0
18.440 Final Exam: 100 points
Carefully and clearly show your work on each problem (without
writing anything that is technically not true) and put a box
around each of your nal computations.
1. (10 points) Let X be the number on a standard die roll (i.e.,
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
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)
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
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
Fall 2012 18.440 Final Exam: 100 points
Carefully and clearly show your work on each problem (without
writing anything that is technically not true) and put a box
around each of your nal computations.
1. (10 points) Lisas truck has three states: broken (i
Name
18.05 Exam 2
No books or calculators. You may have one 46 notecard with any information you like on it.
7 problems, 7 pages
Use the back side of each page if you need more space.
Simplifying expressions: You dont need to simplify complicated expressi