36-225 Handout for Lecture # 9
September 15, 2008
1. A new method (method B) for teaching a certain industrial skill was developed, and it was found that there is 90% chance of successfully learning t
36-225 Handout for Lecture # 7
September 10, 2008
1. The information you get with a certain prescription drug states: There is 10% chance of experiencing headache (H) There is 15% chance of experienci
36-225 - Handout for Lecture # 5 September 5, 2008 Last time.
Axioms of Probability 1. P(A) 0 2. P(S) = 1 3. A B = = P(A B) = P(A) + P(B) If S has an infinite number of outcomes. 4. Let A1, A2, A3, .
Lecture #1 (8/25/08)
STAT 36-225, Fall 2008
I. Probability is not always intuitive.
1. Let's Make a Deal As a motivating example behind the discussion of probability, we'll investigate the Let's Make
36-225 Introduction to Probability Theory
Fall 2015
Instructor
Peter Freeman
Office
BH 229G
Email
[email protected]
9:30 AM
10:20 AM
Office Hours
Tu 3-5 and Th 2-5
(or by appointment)
Lecture
MWF
Doher
1. (8 points) Let U = 21.11 Y, where the Y,- are iid draws from a Geometric(0.5) distribution. What
is the variance of U?
Viv] %1Vl
eta] Viki-.3
Viol
2. (8 points) You are to sample data randomly from
1. (8 points) Let U = i 2; Yi, Where the Y; are iid draws from a Uniform(0,1) distribution. What is
the variance of U ?
\ILU] VY17\%;b;] VEY
Viall VEGl viml = iii
(a)
2. (8 points) You make 64 _iid dr
1. (8 points) Let U = zz; 1, where the Y,- are iid draws from a Gamma(2,1) distribution. What is
the variance of U?
2. (8 points) You make 81_iid draws from a distribution with mean 10 and standard de
Tear @ SOLUUON SET
1. (6 points overall) Warmup question: assume you are working with a gamma distribution with
E[Y] = 5 and V[Y] = 10. (a) (4 points) What are the values of a and ? (b) (4 points) Wha
TE 5r SOLQTDN SE T
non-1am
1. (4 points) Warm-up question. You are givenlprobabilities for events A and B. You can use these to
compute P(A ['1 B) if and only if you make what assumption about the two
TEST CED Soc-anon SET
1. (6 points overall) Warmup question: assume you are working with a gamma distribution with
E[Y] = 3 and V[Y] = 9. (a) (4 points) What are the values of a and 6? (b) (4 points)
Fig 51' $0Luou~l SET
1. (6 points overall) Warm-up question: assume you are working with a gamma distribution with
E[Y] = 3 and V[Y] = 9. (a) (4 points) What are the values of a and ,6? (b) (4 points)
TE$T (B) Soufe S ET"
1. (4 points) Warm-up question. You are given (nonzero!) probabilities for events A and B. You can use these
to compute P(A n B) if and only if you make What assumption about the
TEST SOLunoM SET
1. (4 points) Warmup question. You are given (nonzero!) probabilities for events A and B. You can
use these to compute P(A n B) if and only if you make what assumption about the two e
15-150 Spring 2015
Homework 06
Out: Wednesday, 18 February 2015
Due: Tuesday, 24 February 2015 at 23:59 EST
NOTE: Since this hw is due right before the midterm, late days are not
permitted for this hw
15-150 Spring 2015
Homework 01
Out: Wednesday, 14 January 2015
Due: Tuesday, 20 January 2015 at 23:59 EST
1
Introduction
Welcome to 15-150! This assignment introduces the course infrastructure and the
36-225 Introduction to Probability Theory Fall 2015
Homework 8
Due Friday, November 6th at 9:30 AM in DH 2315
Exercise numbers refer to Wackerly 7. If you are not using the American print edition of W
36-225 Handout for Lecture # 11
September 19, 2008
1. Consider the following two random variables: Y - the daily number of defective products coming out of production line A. X - the daily number of d
36-225 - Handout for Lectures # 13 & 14 September 24 & 26, 2008 Special Discrete Random Variables (Distributions)
I. The Binomial Random Variable (Distribution) Consider an experiment which consists o
36-225 - Handout for Lecture # 16 October 1, 2008
Special Discrete Random Variables - Review
I. The Binomial Random Variable X Bin(n, p). X counts the number of successes out of n independent (Bernoul
36-225 Handout for Lecture # 28
October 29, 2010
1. In the game of roulette a wheel with 38 numbered spaces (18 red, 18 black, 2 green) is spun and ball drops into one of the slots. Suppose Player 1 b
36-225 Handout for Lecture # 23
October 18, 2010
1. Suppose scores on the verbal or math portion of the SAT from a particular year are approximately normally distributed with mean = 500 and standard d
STAT 225 - Homework 9
Due Friday, November 5
Comments: 1. This homework is due Friday, November 5 in class, BEFORE class starts. 2. Please remember staple if you turn in more than one page. 3. You mus
STAT 225 - Homework 8
Due Friday October 29
Comments: 1. This homework is due Friday, October 29 in class, BEFORE class starts. 2. Please remember staple if you turn in more than one page. 3. You must
STAT 225 - Homework 7
Due Friday October 22
Comments: 1. This homework is due Friday, October 22 in class, BEFORE class starts. 2. Please remember staple if you turn in more than one page. 3. You must
STAT 225 - Homework 6
Due Monday October 18
1. This homework is due Monday, October 18 in class, BEFORE class starts. 2. Please remember staple if you turn in more than one page. 3. You must always sh