Section 06. The Bernoulli distribution is a special case where n=1!

Slides:

Advertisements

Similar presentations

Chapter 5 Discrete Probability Distributions 1 Copyright © 2012 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Advertisements

Special random variables Chapter 5 Some discrete or continuous probability distributions.

Why this can be happen to me?. Can you think, who’ll be the faster catch the fish??

Discrete Uniform Distribution

Chapter 6 Some Special Discrete Distributions

Chapter 2 Discrete Random Variables

Today Today: Finish Chapter 4, Start Chapter 5 Reading: –Chapter 5 (not 5.12) –Important Sections From Chapter (excluding the negative hypergeometric.

Probability Distribution

5.1 Sampling Distributions for Counts and Proportions.

Risk Pooling in Insurance If n policies, each has independent probability p of a claim, then the number of claims follows the binomial distribution. The.

CSE 3504: Probabilistic Analysis of Computer Systems Topics covered: Moments and transforms of special distributions (Sec ,4.5.3,4.5.4,4.5.5,4.5.6)

The Poisson Probability Distribution

Bernoulli Distribution

Engineering Probability and Statistics - SE-205 -Chap 3 By S. O. Duffuaa.

Probability theory 2011 Outline of lecture 7 The Poisson process  Definitions  Restarted Poisson processes  Conditioning in Poisson processes  Thinning.

A random variable that has the following pmf is said to be a binomial random variable with parameters n, p The Binomial random variable.

2. Random variables  Introduction  Distribution of a random variable  Distribution function properties  Discrete random variables  Point mass  Discrete.

Discrete Probability Distributions

Discrete Probability Distributions

Section 09.  This table is on page 280 of the Actex manual Distribution of XiDistribution of Y Bernoulli B(1,p)Binomial B(k,p) Binomial.

Class notes for ISE 201 San Jose State University

Section 10.  An insurance policy is a contract between the party that is at risk (the policyholder) and the insurer  The policyholder pays a premium.

The Poisson Probability Distribution The Poisson probability distribution provides a good model for the probability distribution of the number of “rare.

Discrete Probability Distributions. Probability Distributions.

Lecture 4 1 Discrete distributions Four important discrete distributions: 1.The Uniform distribution (discrete) 2.The Binomial distribution 3.The Hyper-geometric.

Poisson Random Variable Provides model for data that represent the number of occurrences of a specified event in a given unit of time X represents the.

Practice Problems Actex 8. Section 8 -- #5 Let T 1 be the time between a car accident and reporting a claim to the insurance company. Let T 2 be the time.

The Negative Binomial Distribution An experiment is called a negative binomial experiment if it satisfies the following conditions: 1.The experiment of.

Probabilistic and Statistical Techniques 1 Lecture 19 Eng. Ismail Zakaria El Daour 2010.

Copyright © 2015 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 C H A P T E R F I V E Discrete Probability Distributions.

Section Copyright © 2014, 2012, 2010 Pearson Education, Inc. Lecture Slides Elementary Statistics Twelfth Edition and the Triola Statistics Series.

Random Variables and Probability Models

Your mail-order company advertises that it ships 90% of its orders within three working days. You select an SRS of 100 of the 5000 orders received in.

Discrete Probability Distributions. Random Variable Random variable is a variable whose value is subject to variations due to chance. A random variable.

JMB Chapter 5 Part 1 EGR Spring 2011 Slide 1 Known Probability Distributions  Engineers frequently work with data that can be modeled as one of.

Math 4030 – 4a Discrete Distributions

Math b (Discrete) Random Variables, Binomial Distribution.

A life insurance company sells a term insurance policy to a 21-year-old male that pays $100,000 if the insured dies within the next 5 years. The probability.

Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Section 5-5 Poisson Probability Distributions.

Methodology Solving problems with known distributions 1.

Probability Distribution

8.2 The Geometric Distribution. Definition: “The Geometric Setting” : Definition: “The Geometric Setting” : A situation is said to be a “GEOMETRIC SETTING”,

4.2 Binomial Distributions

Exam 2: Rules Section 2.1 Bring a cheat sheet. One page 2 sides. Bring a calculator. Bring your book to use the tables in the back.

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

Working with means and variances…. Expected Values… How does an insurance company determine its premiums? Weighs probability of “pay-out” against total.

By Satyadhar Joshi. Content  Probability Spaces  Bernoulli's Trial  Random Variables a. Expectation variance and standard deviation b. The Normal Distribution.

Why do Actuaries Need Maths? By Sami Rahman Introduction: What is an Actuary? Google definition: A person who compiles and analyses statistics and uses.

Practice Problems Actex Sections 6, 7. Section 6 -- #3 A company prices its hurricane insurance using the following assumptions: – In any calendar year,

Probability Generating Functions Suppose a RV X can take on values in the set of non-negative integers: {0, 1, 2, …}. Definition: The probability generating.

Unit 4 Review. Starter Write the characteristics of the binomial setting. What is the difference between the binomial setting and the geometric setting?

Random Probability Distributions BinomialMultinomial Hyper- geometric

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

Statistics -Continuous probability distribution 2013/11/18.

Chapter5 Statistical and probabilistic concepts, Implementation to Insurance Subjects of the Unit 1.Counting 2.Probability concepts 3.Random Variables.

Practice Problems Actex 10. Section #1 An insurance policy pays an individual 100 per day for up to 3 days of hospitalization and 25 per day for.

Math 4030 – 4a More Discrete Distributions

The Poisson Probability Distribution

Functions and Transformations of Random Variables

3.4 The Binomial Distribution

Probability Review for Financial Engineers

Discrete Probability Distributions

Some Discrete Probability Distributions

Part 2: Named Discrete Random Variables

Chapter 5 Some Discrete Probability Distributions.

8.2 The Geometric Distribution

Chapter 3 : Random Variables

Bernoulli Trials Two Possible Outcomes Trials are independent.

The Geometric Distributions

Each Distribution for Random Variables Has:

Presentation transcript:

Section 06

The Bernoulli distribution is a special case where n=1!

The geometric distribution is a special case where r =1!

 DEFINITELY know  Uniform  Binomial  Poisson  Geometric  TRY TO know  Negative Binomial  Hypergeometric  Maybe not  Multinomial

A tour operator has a bus that can accommodate 20 tourists. The operator knows that tourists may not show up, so he sells 21 tickets. The probability that an individual tourist will not show up is.02, independent of all other tourists. Each ticket costs 50, and is non-refundable if a tourist fails to show up. If a tourist shows up and a seat is not available, the tour operator has to pay 100 (ticket cost + 50 penalty) to the tourist. What is the expected revenue of the tour operator?

An actuary has discovered that policyholders are three times as likely to file two claims as to file four claims. If the number of claims filed has a Poisson distribution, what is the variance of the number of claims filed?

A baseball team has scheduled its opening game for April 1. If it rains on April 1, the game is postponed and will be played on the next day that it does not rain. The team purchases insurance against rain. The policy will pay 1000 for each day, up to 2 days, that the opening game is postponed. The insurance company determines that the number of consecutive days of rain beginning on April 1 is a Poisson random variable with mean.6 What is the standard deviation of the amount the insurance company will have to pay?