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PSTAT 120A Probability I

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University of California, Santa Barbara (UCSB)
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MACKGALLOWAY, EduardoMontoya, ENGLANDER, Staff, JANOSENGLANDER, CARTER, TASHMAN, KumarRohini, BONNETT, Chavez, wenjianliu, Wejian, Fang-IChu, OLAFSSONS, Sveinn, Herndon, hohn, roa, Pierre-Oliver Goffard

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3 pages
- PSTAT 120A Assignment 1a Answers
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Summer 2015
- PSTAT W 120A: Solutions for Assignment 1.a August 7, 2015 Lesson 1 1. We will rst note that A and Ac form a partition of the entire sample space. Thus, P(A) P(A) + P(Ac ) c = P(A A ) by Non-Negative Axiom by Addition Axiom = P(S) =1 by Total Probability A
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PSTAT 120A Assignment 1a Answers
1 pages
- Week2sol
- UCSB
- PSTAT
- PSTAT 120A - Fall 2015
- PSTAT 120A: Discussion Session 2 (Oct 6 - Oct 8) Problem 1. Pitman, Appendix A, problems (x) (xi), (xii), (xiii), (xiv). Problem 2. (a) A child has 12 blocks, of which 6 are black, 4 are red, 1 is white, and 1 is blue. If the child puts the blocks in a li
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Week2sol
2 pages
- PSTAT 120A Assignment 1b Answers
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Summer 2015
- PSTAT W 120A: Solutions 1.b August 10, 2015 1. There are three motors available to repair Ralphs vacuum cleaner. Motor #1 has a 65% chance of breaking by the end of the week. Motor #2 has a 25% chance of breaking by the end of the week. Motor #3 has a 5%
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PSTAT 120A Assignment 1b Answers
8 pages
- midtermSveinnSpring2016
- UCSB
- stat for econ
- PSTAT 120A - Spring 2016
- PSTAT 120A Spring 2016 Midterm Name (Print): Discussion Section: Teaching Assistant: Do not turn the page until you are directed to do so. Turn your cellphone off and put it away during the exam period. You have 75 minutes to complete the exam. You ma
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midtermSveinnSpring2016
5 pages
- HW6-Solutions
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Winter 2014
- PSTAT 120A Homework 6 Winter 2016 Due: Thursday, 3/3/2016 by 4:00 pm Problem 1: Suppose that in a group of 10 people, each person has a 0.1 probability of having a certain disease, independently from person to person. Now consider a testing plan where the
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HW6-Solutions
3 pages
- week3sol-3
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Fall 2015
- PSTAT 120A: Discussion Session 3 (Oct 13 - Oct 15) Problem 1. Explain (no need to derive) why the following identities are true for any n and k such that 0 k n: n n (a) k = n k . P n n n (b) n k=0 k = 2 [Hint: recall that the number of subsets of a se
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week3sol-3
33 pages
- Lecture 9
- UCSB
- stat for econ
- PSTAT 120A - Spring 2016
- Lecture 9 Continuous distributions Uniform Random variables Sveinn lafsson [email protected] Continuous Random Variables - So far we have only discussed discrete random variables that can only take values in a discrete set (i.e. a set that contains
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Lecture 9
4 pages
- Final W15
- UCSB
- PSTAT
- PSTAT 120A - Fall 2015
- FINAL EXAM A PSTAT 120A - Winter 2015 By writing my name and signing below I swear that I have not engaged in any form of academic dishonesty or cheating. Name: Signature: Section meeting time: Do not turn the page until you are directed to do so. Turn
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Final W15
2 pages
- hw5-3
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Fall 2015
- PSTAT 120A: HW5 Due Nov 19 at the beginning of class Clearly mark your solutions with your name, the name of your TA, and the time of your discussion session. Staple the pages of your solution set together. Problem 1. The probability density function of a
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hw5-3
1 pages
- Week2
- UCSB
- PSTAT
- PSTAT 120A - Fall 2015
- PSTAT 120A: Discussion Session 2 (Oct 6 - Oct 8) Problem 1. Pitman, Appendix A, problems (x) (xi), (xii), (xiii), (xiv). Problem 2. (a) A child has 12 blocks, of which 6 are black, 4 are red, 1 is white, and 1 is blue. If the child puts the blocks in a li
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Week2
5 pages
- PSTAT 120A Homework 3B Solutions
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Summer 2015
- PSTAT W 120A: Solutions for Assignment 3B August 24, 2015 Lesson 11 Variance 1. We have an experiment that produces a measurement X with probability density function x P (x) -10 0.1 -5 0.2 0 0.3 5 0.2 10 0.2 (a) The expected value of X is E(X) = 10(0.1) 5
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PSTAT 120A Homework 3B Solutions
2 pages
- PSTAT 120A Homework 3A Solutions
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Summer 2015
- PSTAT W 120A: Solutions for Assignment 3A August 28, 2015 Lesson 9 Joint Distributions 1. Suppose that we have a pair of random variables X and Y with joint distribution 2 4 6 Y 2 0.04 0.12 0.24 X 4 0.02 0.06 0.12 6 0.04 0.12 0.24 (a) If we have M = max(X
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PSTAT 120A Homework 3A Solutions
4 pages
- PSTAT 120A Homework 4B Solutions
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Summer 2015
- PSTAT W 120A: Solutions for Assignment 4B September 2, 2015 Lesson 15 Cumulative Distribution Functions 1. The CDF of our random variable X is F (t) = t2 15 25t + 15t2 3t3 4 1 (a) The probability of cfw_ 2 X 1 is Pcfw_ 1 1 X 1 = F (1) F 2 2 1 1 = (15 25
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PSTAT 120A Homework 4B Solutions
5 pages
- Midterm S13
- UCSB
- PSTAT
- PSTAT 120A - Fall 2015
- MIDTERM EXAM A PSTAT 120A - Spring 2013 By writing my name and signing below I swear that I have not engaged in any form of academic dishonesty or cheating. Name: Signature: Section time and TA: Do not turn the page until you are directed to do so. Turn
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Midterm S13
5 pages
- Homework2Sol
- UCSB
- PSTAT
- PSTAT 120A - Fall 2015
- PSTAT 120A: HW2 - Solutions Problem 1. (a) A restaurant oers 15 possible toppings for its pizzas. How many dierent pizzas with 4 dierent toppings can be ordered? (b) How many ways can 5 people stand in line at the restaurant? (c) The restaurant has 12 roo
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Homework2Sol
6 pages
- hw3sol-3
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Fall 2015
- PSTAT 120A: HW3 - Solutions Problem 1. Urn I contains 25 white and 15 black balls. Urn II contains 15 white and 25 black balls. An urn is selected at random and ve balls are drawn randomly from this urn without replacement. If exactly ve of these balls ar
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hw3sol-3
4 pages
- PSTAT 120A Assignment 2b Answers
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Summer 2015
- PSTAT W 120A: Solutions for Assignment 2.b August 18, 2015 Lesson 7 Poisson Approximation 1. A survey of 3300 people asked them whether they liked apple pie. Suppose that the people were all chosen independently with a 99.98% chance of liking apple pie. (
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PSTAT 120A Assignment 2b Answers
6 pages
- hw6sol
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Fall 2015
- PSTAT 120A: HW6 - Solutions Problem 1. Let X be a uniform random variable dened on the interval (0, 1). If Y = 6X 2 6X +1, compute the correlation of X and Y . Are X and Y independent? Are X and Y uncorrelated? Solution: Using the linearity of the covaria
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hw6sol
5 pages
- hw5sol
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Fall 2015
- PSTAT 120A: HW5 - Solutions Problem 1. The probability density function of a continuous random variable X is piecewise linear and is given by 8 1 if 0 < x < 1, > 4, > > 5 x > < , if 1 x < 5, 16 fX (x) = x 5 > 2 , if 5 x < 6, > > > : 0, otherwise. Plot thi
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hw5sol
1 pages
- hw1
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Spring 2008
- The homework has to be stapled. PSTAT 174/274. Homework #1 Name: Due: Score: 10/16/06 at the beginning of the discussion session /10 Credit: People you worked with: Sources consulted(Reference): 1. (2 points each) Consider the time series xt = 1
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hw1
5 pages
- Homework5Sol
- UCSB
- PSTAT
- PSTAT 120A - Fall 2015
- PSTAT 120A: HW5 - Solutions Problem 1. The probability density function of a continuous random variable X is piecewise linear and is given by 1 if 0 < x < 1, 4, 5x , if 1 x < 5, 16 fX (x) = x5 2 , if 5 x < 6, 0, otherwise. Plot this probability densi
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Homework5Sol
7 pages
- Homework 6 w/ Solutions- Moments
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Winter 2015
- PSTAT 120A Probability theory UCSB Professor Chavez Homework Assignment # 6 Homework assignment # 6 will be collected on Thursday 2/26/2015 at the beginning of lecture time. Only two randomly chosen exercises will be graded. The section quiz on Wednesday
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Homework 6 w/ Solutions- Moments
2 pages
- HW 4
- UCSB
- stat for econ
- PSTAT 120A - Spring 2016
- PSTAT 120A. Probability and Statistics I. Winter 2016 Homework 4, due February 10 Problems from old actuarial exams in Probability are marked by an asterisk. Problem 1. Calculate P(X 4) for: (i) X Bin(3, 0.7); (ii) X Bin(5, 0.7); (iii) X Poi(1). Problem 2
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HW 4
5 pages
- HW 4 Solution
- UCSB
- stat for econ
- PSTAT 120A - Spring 2016
- PSTAT 120A. Probability and Statistics I. Winter 2016 Homework 4 Solution, due February 10 Problems from old actuarial exams in Probability are marked by an asterisk. Problem 1. Calculate P(X 4) for: (i) X Bin(3, 0.7); (ii) X Bin(5, 0.7); (iii) X Poi(1).
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HW 4 Solution
4 pages
- HW 3 Solution
- UCSB
- stat for econ
- PSTAT 120A - Spring 2016
- PSTAT 120A. Probability and Statistics I. Winter 2016 Homework 3 Solution, due February 3 Problems from old actuarial exams in Probability are marked by an asterisk. Problem 1. Let X be the random number on a die: from 1 to 6. (i) What is the distribution
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HW 3 Solution
27 pages
- Lecture 1 (6)
- UCSB
- stat for econ
- PSTAT 120A - Spring 2016
- Lecture 1 Set Theory, Introduction to Probability, Sample Spaces, The Addition Law Sveinn lafsson [email protected] Sample Space Sample Space : the set of all possible outcomes for a random experiment which produces unpredictable outcomes represent
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Lecture 1 (6)
34 pages
- Lecture 4 (1)
- UCSB
- stat for econ
- PSTAT 120A - Spring 2016
- Lecture 4 Permutations and Combinations Sveinn lafsson [email protected] Permutations We use Permutations when we are interested in the number of possible ways to choose a subset of objects, and ORDER IS IMPORTANT (Ex: a,b,b,a is not the same as b,
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Lecture 4 (1)
5 pages
- HW 2 Solution
- UCSB
- stat for econ
- PSTAT 120A - Spring 2016
- PSTAT 120A. Probability and Statistics I. Winter 2016 Homework 2 Solution, due January 20 Problems from old actuarial exams are marked by an asterisk. Problem 1. Pick a random number from 1 to 1000. Find the probability that this number is not divisible b
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HW 2 Solution
3 pages
- HW 1 Solution
- UCSB
- stat for econ
- PSTAT 120A - Spring 2016
- UC Santa Barbara. PSTAT 120A. Probability and Statistics I. Winter 2016. HW 1 Solution Homework 1 Solution, due January 13 Problem 1. There are 8 apartments for 6 people. Each person chooses one apartment, and each apartment can host no more than one pers
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HW 1 Solution
5 pages
- Lecture 4
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Winter 2015
- PROBABILITY AND DISCRETE-TIME STOCHASTIC PROCESSES 17 The variance is much smaller. You get the same average return but with low risk. This is called diversification; this is essential for finance and insurance. This is why insurance companies need large
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Lecture 4

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2 pages
- PSTAT 120A Week 9 Handout.pdf
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Winter 2015
- WEEK 9: JOINTLY DISTRIBUTED R.V. PSTAT 120A - S17 Created by Professor Hohn 1. (Ross, 7.4) If X and Y have joint density function fx,y(x,y) = jj i/y (a) Find E[XY]. (b) Find E[X]. (c) Find E[Y]. 1 0 < y < 1,0 < x < y otherwise 2. Suppose that you have a b
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PSTAT 120A Week 9 Handout.pdf
284 pages
- PSTAT 120A Lectures 1-10 notes.pdf
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Winter 2015
- Lecture 1 Sample spaces, Introduction to Probability, the Law of Addition Sveinn lafsson [email protected] Sample Space Sample space : A set containing all possible outcomes for a random experiment represents a single element (outcome) in the samp
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PSTAT 120A Lectures 1-10 notes.pdf
2 pages
- PSTAT 120A Week 5 Handout.pdf
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Winter 2015
- WEEK 5: DISCRETE RVS AND EXPECTED VALUE PSTAT 120A - S17 Created by Professor Hohn 1. You have a fair coin, and you want to take your professors money. You ask the professor to play a gambling game with you. The gambling game is designed as follows: You c
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PSTAT 120A Week 5 Handout.pdf
2 pages
- PSTAT 120A Week 8 Handout.pdf
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Winter 2015
- WEEK 8: NORMAL R.V. PSTAT 120A - S17 Created by Professor Hohn 1. Suppose that the height, in inches, of a 25-month-old Charmander (a lizard Pokemon) is a normal random variable with parameters yU = 24 and a2 = 16. (a) What fraction of Charmanders are tal
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PSTAT 120A Week 8 Handout.pdf
2 pages
- PSTAT 120A Week 1 Handout.pdf
- UCSB
- PROBABILITY AND STATISTICS I
- PSTAT 120A - Winter 2015
- WEEK 1: COMBINATORICS PSTAT 120A - Spring 2017 Created by Professor Hohn 1. Hogwarts School was invited to play at an international quidditch competition. At the school, Hogwarts has 12 Chasers, 8 Beaters, 4 Keepers, and 4 Seekers of which to choose 7 pla
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PSTAT 120A Week 1 Handout.pdf

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