Dr. Ali Moshtagh Probability Problems

Slides:

Advertisements

Similar presentations

Probability Distribution

Advertisements

Let X 1, X 2,..., X n be a set of independent random variables having a common distribution, and let E[ X i ] = . then, with probability 1 Strong law.

Genetic Statistics Lectures （５） Multiple testing correction and population structure correction.

HYPOTHESIS TESTING Four Steps Statistical Significance Outcomes Sampling Distributions.

2003/02/13 Chapter 4 1頁1頁 Chapter 4 : Multiple Random Variables 4.1 Vector Random Variables.

4. Convergence of random variables  Convergence in probability  Convergence in distribution  Convergence in quadratic mean  Properties  The law of.

Samples vs. Distributions Distributions: Discrete Random Variable Distributions: Continuous Random Variable Another Situation: Sample of Data.

2003/04/24 Chapter 5 1頁1頁 Chapter 5 : Sums of Random Variables & Long-Term Averages 5.1 Sums of Random Variables.

Chapter 5. Operations on Multiple R. V.'s 1 Chapter 5. Operations on Multiple Random Variables 0. Introduction 1. Expected Value of a Function of Random.

Normal and Sampling Distributions A normal distribution is uniquely determined by its mean, , and variance,  2 The random variable Z = (X-  /  is.

Probability and Statistics Dr. Saeid Moloudzadeh Axioms of Probability/ Basic Theorems 1 Contents Descriptive Statistics Axioms of Probability.

1 Conditional Probability and Bayes’ Theorem Dr. Jerrell T. Stracener, SAE Fellow EMIS 7370 STAT 5340 Probability and Statistics for Scientists and Engineers.

AP Statistics Chapter 9 Notes.

Advanced Higher Statistics Data Analysis and Modelling Hypothesis Testing Statistical Inference AH.

Probability and Statistics Dr. Saeid Moloudzadeh Counting Principle/ Permutations 1 Contents Descriptive Statistics Axioms of Probability.

1 SMU EMIS 7364 NTU TO-570-N Control Charts for Attributes Data Updated: Statistical Quality Control Dr. Jerrell T. Stracener, SAE Fellow.

Chapter 7 Sampling and Sampling Distributions ©. Simple Random Sample simple random sample Suppose that we want to select a sample of n objects from a.

Probability and Statistics Dr. Saeid Moloudzadeh Random Variables/ Distribution Functions/ Discrete Random Variables. 1 Contents Descriptive.

MATH – High School Common Core Vs Kansas Standards.

IE 300, Fall 2012 Richard Sowers IESE. 8/30/2012 Goals: Rules of Probability Counting Equally likely Some examples.

Probability and Statistics Dr. Saeid Moloudzadeh Joint Distribution of Two Random Variables/ Independent Random Variables 1 Contents Descriptive.

Topic 6: The distribution of the sample mean and linear combinations of random variables CEE 11 Spring 2002 Dr. Amelia Regan These notes draw liberally.

Probability and Statistics Dr. Saeid Moloudzadeh Uniform Random Variable/ Normal Random Variable 1 Contents Descriptive Statistics Axioms.

Review of Statistical Terms Population Sample Parameter Statistic.

1 Sampling distributions The probability distribution of a statistic is called a sampling distribution. : the sampling distribution of the mean.

11.7 Continued Probability. Independent Events ► Two events are independent if the occurrence of one has no effect on the occurrence of the other ► Probability.

Central Limit Theorem Let X 1, X 2, …, X n be n independent, identically distributed random variables with mean  and standard deviation . For large n:

Lecture 19 Dr. MUMTAZ AHMED MTH 161: Introduction To Statistics.

Probability and Statistics Dr. Saeid Moloudzadeh Poisson Random Variable 1 Contents Descriptive Statistics Axioms of Probability Combinatorial.

ELEC 303 – Random Signals Lecture 14 – Sample statistics, Limit Theorems Dr. Farinaz Koushanfar ECE Dept., Rice University Oct 21, 2010.

Statistics and probability Dr. Khaled Ismael Almghari Phone No:

BUS 308 Week 2 Quiz Check this A+ tutorial guideline at 1. How is the sum of squares unlike.

Sampling and Sampling Distributions

Lot-by-Lot Acceptance Sampling for Attributes

Advanced Higher Statistics

Significance Test for the Difference of Two Proportions

Chain Rules for Functions of Several Variables

R. E. Wyllys Copyright 2003 by R. E. Wyllys Last revised 2003 Jan 15

8.1 The Binomial Distributions

One sample t-test and z-test

Extensions and Restrictions of Turing Machines

Tech 31: Unit 4 Control Charts for Attributes

JUS 510 Competitive Success/snaptutorial.com

JUS 510 Education for Service-- snaptutorial.com.

JUS 510 Education for Service/tutorialrank.com

JUS 510 Teaching Effectively-- snaptutorial.com

AP Statistics: Chapter 7

Random Sampling Population Random sample: Statistics Point estimate

Interval Estimation.

Statistics 1: Elementary Statistics

Binomial Probability Distribution

Sampling Distribution

Sampling Distribution

Introduction to Probability & Statistics The Central Limit Theorem

ASV Chapters 1 - Sample Spaces and Probabilities

Lecture Slides Elementary Statistics Twelfth Edition

Statistics Applied to Economics I

From Simulations to the Central Limit Theorem

Sampling Distributions

COnDITIONAL Probability

Section 11.7 Probability.

MBA 510 Review for Exam 1 February 8

6.3 Sampling Distributions

Algorithms Lecture # 01 Dr. Sohail Aslam.

Review of Hypothesis Testing

2015 Question 3 Intent of Question

Multiplication Law for Several Events

Presentation transcript:

Dr. Ali Moshtagh Probability Problems 9/22/2018

The Michigan Molding Co. The Michigan Molding Co. produces two-color legend plates for aircraft cockpits using four machines ( W, X, Y, and Z ). After quality-control inspection, the plates are graded as A, acceptable; B, needs repair; and C, can be scrapped. 1 9/22/2018

A sample of 1,000 legend plates revealed the following results: 2

State in symbols, the probability that a legend plate selected at random was produced by machine W. was produced by machine X and needs repair. Needs repair given that it was produced by machine Y. (restricted to plates produced by machine W) is acceptable. was either produced by machine Z or can be scrapped. 3

State in words the meaning of each of the following P ( B | Z ) P ( A  Y ) P ( B U X ) 4

Compute the probability that a plate selected at random was produced by machine Z. was produced by machine X and is acceptable. is acceptable, given that it was produced by machine X. is either in need of repair or was produced by machine W. 5

Use the addition theorem or multiplication theorem, as appropriate, to compute the following probabilities P ( Y  B ) P ( C U X ) P ( A  C ) 6

Determine if the variables (machine and grade) are statistically independent and show why or why not. 7