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Penn State | STAT 318
Elementary Probability
Professors
• Kurum, Esra,
• ,
• Tabacu, Lucia Mari,
• Artemiou, Andreaslee, Hyang Min,
• Artemiou, Andreas,
• Scott Roths

#### 38 sample documents related to STAT 318

• Penn State STAT 318
Final Exam Review 7:00-9:00pm, Dec 17; Willard 62 You can bring two double-sided cheating sheets and a calculator with you in the exam. The exam is comprehensive, consisting of five written problems. But Chapter 3-5 will be the emphasis. Please g

• Penn State STAT 318
Midterm Exam 2 Review 1:25-2:15pm, Nov,10; Room 60 Willard You can bring a double-sided cheating sheet and a calculator with you in the exam. The exam covers all sections in Chapter3 and consists of five written problems. Please go through all ex

• Penn State STAT 318
Midterm Exam 1 Review You can bring a double-sided cheating sheet and a calculator with you in the exam. The exam will consist of multiple choices and written problems. Please go through all examples discussed in class and the homework problems. S

• Penn State STAT 318
Stat 318 Midterm 2 Chapters 3 Friday, November 16th 2007 Before opening the paper: Write your name, PSU ID # and sign at the space provided below: NAME : _ PSU ID # : __ SIGNATURE : _ Grade: Problem 1: Problem 2: Problem 3: Problem 4: Bonus Points:

• Penn State STAT 318
Quiz #5 Friday, October 5th NAME: _ Grade: _ out of 25. You have 30 minutes to complete this Quiz. This Quiz is a closed book and Notes exam Exercise 2 is on the other side of the test. Exercise 1: (10 points) Let\'s say that there are only 5 airline

• Penn State STAT 318
Quiz #6 Friday, October 12th NAME: _ Grade: _ out of 25. You have 20 minutes to complete this Quiz. This Quiz is a closed book and Notes exam Exercise 1: (30 points) Let say that the probability that someone will fail X number of classes during the

• Penn State STAT 318
Quiz #7 Friday, October 19th NAME: _ Grade: _ out of 25. You have 30 minutes to complete this Quiz. This Quiz is a closed book and Notes exam. You may use the Tables I have distributed in class, though. Exercises 3 and 4 are on the reverse side. Exe

• Penn State STAT 318
Lecture 21 Chapter 4 Wednesday, November 5th This Lecture We will talk what happens when we know the pdf of a random variable and then we want to learn the pdf of another variable. There is only one theorem in this section. If the conditions in each case

• Penn State STAT 318
Lecture 20 Chapter 4 Monday, November 3rd Gamma function In this lecture we will use a lot the gamma function. For > 0 the gamma function is defined as follows: -1 - x ( ) = x e dx 0 Properties of gamma function: ( ) = ( - 1) ( - 1) For integer n, ( n ) =

• Penn State STAT 318
Lecture 19 Chapter 4 Wednesday, October 29th Normal distribution \"Normal distribution is a statistical unicorn\" It is the most important distribution in statistics. Most of the random variables out in nature fit naturally to normal distribution Of course,

• Penn State STAT 318
Lecture 18 Chapter 4 Monday, October 27th Expected value The expected value of a continuous random variable X with pdf f(x) is x = E ( X ) = - xf ( x ) dx Example 4.10 page 168 Properties of expected value If X is a continuous random variable with pdf f(

• Penn State STAT 318
Lecture 17 Chapter 4 Wednesday, October 22nd Continuous random variable In Chapter 3 we have seen that a continuous random variable is one that can take any possible value in a given interval. Example: People weight People height Distance between two citi

• Penn State STAT 318
Lecture 16 Chapter 3 Monday, October 20th Poisson Distribution A random variable X is said to have a Poisson distribution with parameter > 0 if the pmf of X is e p ( x) = x! - x Where x=0,1,2,. Cases There are many cases where a random variable is said to

• Penn State STAT 318
Lecture 15 Chapter 3 Wednesday, October 15th Hypergeometric Experiment A hypergeometric experiment is one that satisfies: There is a population of N elements Each element can be characterized as a success or a failure We select a sample of n elements with

• Penn State STAT 318
Lecture 14 Chapter 3 Monday, October 13th Binomial experiment A binomial experiment is one that satisfies the four following requirements: The experiment consists of a sequence of n smaller experiment called trials, where n is fixed in advance of the expe

• Penn State STAT 318
Lecture 13 Chapter 3 Wednesday, October 8th Moments The expected value of a power of a random variable is called moment (or moment around 0) First moment or Expected value E(X) Second moment E(X2) Third moment E(X3) and so on. Central moments Central mome

• Penn State STAT 318
Lecture 12 Chapter 3 Monday, October 6th Example In State College there are 10000 families. I asked them how many kids they have and I get the following answers: 0 kids: 900 families 1 kid: 1700 families 2 kids: 4000 families 3 kids: 2100 families 4 kids:

• Penn State STAT 318
Lecture 11 Chapter 3 Wednesday, October 1st Probability distribution The probability distribution or probability mass function (pmf) of a discrete random variable is defined as a rule that assigns probability to all possible outcomes of the random variabl

• Penn State STAT 318
Lecture 10 Chapter 3 Monday, September 29th Random variables For a given random space of an experiment, a random variable is a function that associates a number with each outcome Example: How many credits you have this semester? How old are you? How many

• Penn State STAT 318
Lecture 9 Chapter 2 Monday, September 22th Independence Two events A and B are independent if P ( A / B ) = P ( A) and they are dependent otherwise. That means they are independent if knowing that event B has occurred this doesn\'t affect the probability o

• Penn State STAT 318
Lecture 8 Chapter 2 Wednesday, September 17th Probability Until now we have learn how to assign probabilities on sets that are consisted of simple events without assuming that we know anything regarding the environment that might affect the probability. C

• Penn State STAT 318
Lecture 7 Chapter 2 Monday, September 15th Counting Techniques Last lecture we have seen that if a set A contains N(A) simple events, and the total number of possible simple events is N N ( A) then: P ( A) = It is easy to count this if number N is small.

• Penn State STAT 318
Lecture 6 Chapter 2 Wednesday, September 10th Probability The objective of probability is to assign to each event A, a number P(A), which is called probability of the event A and will give a precise measure of the chance that A will occur. Axiom of Probab

• Penn State STAT 318
Lecture 5 Chapter 2 Monday, September 8th Probability What is probability? Probability refers to the study of uncertainty and randomness Definitions Experiment is any process whose outcome is subject to uncertainty. Sample space of an experiment is the se

• Penn State STAT 318
Lecture 4 Chapter 1 Wednesday, September 3rd Measures of variability Range is the range of values Formula: Range = maximum minimum Example: I give a test in a class and I take a sample of 6 students. The grades are: 50, 70, 64, 94, 78, 88. Find the range

• Penn State STAT 318
Lecture 3 Chapter 1 Friday, August 29th Measures What might be interesting features of the data that we might want to know about? Measures In this class we will learn two categories of measures: Measures of location Mean Median Trimmed mean Percentiles Me

• Penn State STAT 318
Lecture 2 Chapter 1 Wednesday, August 27th Stem-and-Leaf Diagram Steps: Select the stem values List stem values in a vertical column Record the leaf for every observation next to the corresponding stem value Write the key Example I ask 20 professors in th

• Penn State STAT 318
Lecture 1 Chapter 1 Monday, August 25th Introduction What is Statistics? Where do we use Statistics? Definitions Data is a collection of facts Population is a well defined collection of objects that are of interest When we have available information for a

• Penn State STAT 318
Hints: Homework 3 Stat 318, Spring 2003 1. 2.30 a For a Poisson process with rate , the number of events occurring in time interval of length follows a Poisson distribution with parameter . For a Poisson distribution with parameter , the maximum
http://www.stat.psu.edu/~jiali/course/stat318/homework/hints3.pdf

• Penn State STAT 318
Stat318 Fall2003 Chapter 2: Random Variables (contd) Section 2.2: Continuous Random Variables In the first part of this chapter, we talked about Discrete Random Variables. The support was a finite set of positive integers {0,1,., n} or a countably i
http://www.stat.psu.edu/~msarr/stat318-fall04/classnotes2b.pdf

• Penn State STAT 318
Fall 2004: Stat 318 Midterm I Friday October 1, 2004 In-class Exam from 1:25pm to 2:15pm Problem 1: (25 points) A software development company has three jobs to do. Two of the jobs require 3 programmers and the other requires 4 programmers. The compa
http://www.stat.psu.edu/~msarr/stat318-fall04/midterm1Fall04.pdf

• Penn State STAT 318
(courtesy of Hogg & Tanis, 6th Edition, Probability and Statistical Inference.) Table of some Discrete Distributions [STAT 318]: Probability Mass Function f ( x) = P( X = x) p x (1 p )1 x x = 0 ,1 Random Variable X (parameters) Bernoulli X ~ Ber (
http://www.stat.psu.edu/~msarr/stat318-fall04/discrete.pdf

• Penn State STAT 318
Stat318 Fall2003 Chapter 2: Random Variables (contd) Section 2.2: Continuous Random Variables In the first part of this chapter, we talked about Discrete Random Variables. The support was a finite set of positive integers {0,1,., n} or a countably i
http://www.stat.psu.edu/~msarr/stat318/2.pdf

• Penn State STAT 318
FORMULA SHEET: Chapter 1: Probability Laws of set theory: A B = B A , A B = B A :commutative law ( A B) C = A ( B C ) , ( A B) C = A ( B C ) : associative law ( A B) C = ( A C ) ( B C ) , ( A B) C = ( A C ) ( B C ) : distri
http://www.stat.psu.edu/~msarr/stat318-fall04/formulaStat318.pdf

• Penn State STAT 318
Stat 318-Fall 2003. Chapter 1: Probability Section 1.1: Introduction The study of probability is an old science born out of the gambling (games of chance) rooms of Western Europe. But the theory of probability as a mathematical discipline (axiomatiza
http://www.stat.psu.edu/~msarr/stat318-fall04/Classnotes1.pdf

• Penn State STAT 318

http://www.stat.psu.edu/~msarr/stat318/n01table.pdf

• Penn State STAT 318
Stat318 Fall2003 Chapter 5: Limit Theorems Section 5.1: Introduction Let X 1 ,., X n be n independent random variables and S n = X i = X 1 + . + X n i =1 n As n , what will be the limiting behavior of S n ? Section 5.2: The Law of Large Numbers
http://www.stat.psu.edu/~msarr/stat318/classnotes5.pdf

• Penn State STAT 318
Hints: Homework 1 Stat 318, Spring 2003 1. 1.19 b: To count the number of subcommittees with ve members combination covering all the four ethnic groups, note that one and only one ethnic group provides two members, and all the other ethnic groups pr
http://www.stat.psu.edu/~jiali/course/stat318/homework/hints1.pdf