In-Class Exercise: Geometric and Negative Binomial Distributions

Slides:

Advertisements

Similar presentations

Normal Approximations to Binomial Distributions Larson/Farber 4th ed1.

Advertisements

EXAMPLE 3 Construct a binomial distribution Sports Surveys

6.2 Construct and Interpret Binomial Distributions

The Practice of Statistics

Binomial probability model describes the number of successes in a specified number of trials. You need: * 2 parameters (success, failure) * Number of trials,

EXAMPLE 1 Construct a probability distribution

EXAMPLE 1 Construct a probability distribution Let X be a random variable that represents the sum when two six-sided dice are rolled. Make a table and.

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.

Exercise Exercise3.1 8 Exercise3.1 9 Exercise

Chapter 3-Normal distribution

Bernoulli Distribution

Exercise Exercise Exercise Exercise

Exercise Exercise Exercise Exercise

Exercise Exercise6.1 7 Exercise6.1 8 Exercise6.1 9.

Chapter 5 Probability Distributions

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

Lesson #13 The Binomial Distribution. If X follows a Binomial distribution, with parameters n and p, we use the notation X ~ B(n, p) p x (1-p) (n-x) f(x)

Chapter 5 Discrete Random Variables and Probability Distributions

STARTER The probability that a particular page in a maths book has a misprint is 0.2. Find the probability that of 12 pages in the book: 4 of them have.

1 The probability that a medical test will correctly detect the presence of a certain disease is 98%. The probability that this test will correctly detect.

Mutually Exclusive: P(not A) = 1- P(A) Complement Rule: P(A and B) = 0 P(A or B) = P(A) + P(B) - P(A and B) General Addition Rule: Conditional Probability:

381 Discrete Probability Distributions (The Binomial Distribution) QSCI 381 – Lecture 13 (Larson and Farber, Sect 4.2)

Lesson 12-1 Algebra Check Skills You’ll Need 12-4

The Binomial Distribution

Warm-up Grab a die and roll it 10 times and record how many times you roll a 5. Repeat this 7 times and record results. This time roll the die until you.

Section 5.1 Expected Value HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc. All rights.

Section Binomial Distributions AP Statistics January 12, 2009 CASA.

The Practice of Statistics Third Edition Chapter 8: The Binomial and Geometric Distributions 8.1 The Binomial Distribution Copyright © 2008 by W. H. Freeman.

Binomial Distributions. Quality Control engineers use the concepts of binomial testing extensively in their examinations. An item, when tested, has only.

6.2 Homework Questions.

Starter: After selling Lotto tickets for 5 years, an agent knows that weekly sales are normally distributed with a mean of $3500 and a standard deviation.

Methodology Solving problems with known distributions 1.

Joe,naz,hedger.  Factor each binomial if possible. Solution: Factoring Differences of Squares.

4.3 Discrete Probability Distributions Binomial Distribution Success or Failure Probability of EXACTLY x successes in n trials P(x) = nCx(p)˄x(q)˄(n-x)

Normal Approximations to Binomial Distributions.  For a binomial distribution:  n = the number of independent trials  p = the probability of success.

6.2 BINOMIAL PROBABILITIES.  Features  Fixed number of trials (n)  Trials are independent and repeated under identical conditions  Each trial has.

12.6 – Probability Distributions. Properties of Probability Distributions.

Section 5.2: PROBABILITY AND THE NORMAL DISTRIBUTION.

TRAFFIC MODELS. MPEG2 (sport) Voice Data MPEG2 (news)

Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1 Chapter Normal Probability Distributions 5.

Hypergeometric Distributions Remember, for rolling dice uniform Rolling a 4 P(4) = 1/6 binomial Rolling a 7 P(pair) = 6/36 geometric Rolling a pair P(pair)

MATH Test Review 1. The senior class of a high school has 350 students. How many ways can they select a committee of 5 students?

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.

PROBABILITY AND STATISTICS WEEK 5 Onur Doğan. The Binomial Probability Distribution There are many experiments that conform either exactly or approximately.

May 2006 Question 2  The head circumference of 3-year-old boys is known to be Normally distributed with mean 49.7cm and standard deviation 1.6cm.  Find.

12.SPECIAL PROBABILITY DISTRIBUTIONS

Normal Approximation to the Binomial Distribution.

Warm Up Describe a Binomial setting. Describe a Geometric setting. When rolling an unloaded die 10 times, the number of times you roll a 6 is the count.

8.2 The Geometric Distribution 1.What is the geometric setting? 2.How do you calculate the probability of getting the first success on the n th trial?

Chapter 5 Normal Probability Distributions.

Probability Review for Financial Engineers

Normal Approximations to the Binomial Distribution

Probability Distribution – Example #2 - homework

Useful Discrete Random Variable

Binomial Distributions

Section Binomial Distributions

Chapter 4 Discrete Probability Distributions.

Section 8.2 Geometric Distributions

MSV 40: The Binomial Mean and Variance

Discrete Probability Distributions

Ch. 6. Binomial Theory.

Cumulative Distribution Function

Binomial Distribution: Inequalities for cumulative probabilities

Section 8.2 Geometric Distributions

Chapter 5 Normal Probability Distributions.

2.5 Apply the Remainder and Factor Theorem

Geometric Distribution

Presentation transcript:

In-Class Exercise: Geometric and Negative Binomial Distributions 3-74. In a clinical study, volunteers are tested for a gene that has been found to increase the risk for a disease. The probability that a person carries the gene is 0.1. What is the probability that 4 or more people will have to be tested before 2 with the gene are detected? How many people are expected to be tested before 2 with the gene are detected?

Solution Let X be the number of people tested before two are found with gene X has a negative binomial distribution with r = 2 and p = 0.1. Part a) asks for P(X ≥ 4) Part b) asks for E(X)

Solution