MATH 2311 Section 3.3.

Slides:

Advertisements

Similar presentations

Binomial and geometric Distributions—CH. 8

Advertisements

AP Statistics 51 Days until the AP Exam

C HAPTER 8 Section 8.2 – The Geometric Distribution.

Problems Problems 4.17, 4.36, 4.40, (TRY: 4.43). 4. Random Variables A random variable is a way of recording a quantitative variable of a random experiment.

Chapter – Binomial Distributions Geometric Distributions

AP Statistics: Section 8.1A Binomial Probability.

Binomial & Geometric Random Variables

Chapter 8 Binomial and Geometric Distributions

Chapter 8 The Binomial and Geometric Distributions

Quiz 4  Probability Distributions. 1. In families of three children what is the mean number of girls (assuming P(girl)=0.500)? a) 1 b) 1.5 c) 2 d) 2.5.

A multiple-choice test consists of 8 questions

Binomial & Geometric Random Variables §6-3. Goals: Binomial settings and binomial random variables Binomial probabilities Mean and standard deviation.

Notes – Chapter 17 Binomial & Geometric Distributions.

1 Chapter 8: The Binomial and Geometric Distributions 8.1Binomial Distributions 8.2Geometric Distributions.

Binomial Distributions Calculating the Probability of Success.

The Binomial Distribution. Binomial Experiment.

Chapter 8 Day 1. The Binomial Setting - Rules 1. Each observations falls under 2 categories we call success/failure (coin, having a child, cards – heart.

Chapter 8 Binomial and Geometric Distributions

AP Statistics: Section 8.2 Geometric Probability.

Unit 5 Section 5-4 – Day : The Binomial Distribution  The mean, variance, and standard deviation of a variable that has 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 6.3 Binomial Distributions. A Gaggle of Girls Let’s use simulation to find the probability that a couple who has three children has all girls.

P. STATISTICS LESSON 8.2 ( DAY 1 )

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.

Bernoulli Trials Two Possible Outcomes –Success, with probability p –Failure, with probability q = 1  p Trials are independent.

Binomial Experiment A binomial experiment (also known as a Bernoulli trial) is a statistical experiment that has the following properties:

Binomial Probability Distribution

COMP 170 L2 L17: Random Variables and Expectation Page 1.

1 Since everything is a reflection of our minds, everything can be changed by our minds.

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

At the end of the lesson, students can: Recognize and describe the 4 attributes of a binomial distribution. Use binompdf and binomcdf commands Determine.

Ch. 17 – Probability Models (Day 1 – The Geometric Model) Part IV –Randomness and Probability.

The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers CHAPTER 6 Random Variables 6.3 Binomial and Geometric.

The Binomial Distributions

Section Binomial Distributions AP Statistics

Bernoulli Trials, Geometric and Binomial Probability models.

Chapter 6: Random Variables

16-3 The Binomial Probability Theorem. Let’s roll a die 3 times Look at the probability of getting a 6 or NOT getting a 6. Let’s make a tree diagram.

MATH 2311 Section 3.2. Bernoulli Trials A Bernoulli Trial is a random experiment with the following features: 1.The outcome can be classified as either.

AP Statistics Section 8.2: The Geometric Distribution.

Section 6.3 Geometric Random Variables. Binomial and Geometric Random Variables Geometric Settings In a binomial setting, the number of trials n is fixed.

+ Chapter 8 Day 3. + Warm - Up Shelly is a telemarketer selling cookies over the phone. When a customer picks up the phone, she sells cookies 25% of the.

Introduction We have been looking at Binomial Distributions: A family has 3 children. What is the probability they have 2 boys? A family has 3 children.

The Binomial Distribution Section 8.1. Two outcomes of interest We use a coin toss to see which of the two football teams gets the choice of kicking off.

1. 2 At the end of the lesson, students will be able to (c)Understand the Binomial distribution B(n,p) (d) find the mean and variance of Binomial distribution.

Geometric Distributions Section 8.2. The 4 “commandments” of Geometric Distributions Only 2 outcomes for each trial: success or failure. Only 2 outcomes.

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.

AP Statistics Chapter 8 Section 2. If you want to know the number of successes in a fixed number of trials, then we have a binomial setting. If you want.

CHAPTER 6 Random Variables

MATH 2311 Section 3.3.

Ch3.5 Hypergeometric Distribution

Negative Binomial Experiment

Binomial and Geometric Random Variables

CHAPTER 6 Random Variables

Statistics 1: Elementary Statistics

The Binomial and Geometric Distributions

Lesson 2: Binomial Distribution

Section 8.2: The Geometric Distribution

Statistics 1: Elementary Statistics

Warm Up Imagine a family has three children. 1) What is the probability the family has: 3 girls and 0 boys 2 girls and 1 boy 1 girl and 2 boys 0 girls.

Section 8.2 Geometric Distributions

8.2 The Geometric Distribution

MATH 2311 Section 3.3.

Section 8.2 Geometric Distributions

Warmup The Falcons have won 80% of their games and leading their division. Assume that the result of each game is independent. They have 9 games left.

The Geometric Distributions

Geometric Distribution

The Geometric Distribution

MATH 2311 Section 3.2.

MATH 2311 Section 3.3.

Presentation transcript:

MATH 2311 Section 3.3

Geometric Distributions The geometric distribution is the distribution produced by the random variable X defined to count the number of trials needed to obtain the first success. For example: Flipping a coin until you get a head Rolling a die until you get a 5

A random variable X is geometric if the following conditions are met: 1. Each observation falls into one of just two categories, “success” or “failure.” 2. The probability of success is the same for each observation. 3. The observations are all independent. 4. The variable of interest is the number of trials required to obtain the first success. Notice that this is different from the binomial distribution in that the number of trials is unknown. With geometric distributions we are trying to determine how many trials are needed in order to obtain a success.

Calculating a Geometric Distribution

Mean and Variance

Examples: From text: #8. A quarter back completes 44% of his passes. We want to observe this quarterback during one game to see how many pass attempts he makes before completing one pass. a. What is the probability that the quarterback throws 3 incomplete passes before he has a completion? b. How many passes can the quarterback expect to throw before he completes a pass? c. Determine the probability that it takes more than 5 attempts before he completes a pass. d. What is the probability that he attempts more than 7 passes before he completes one?

Popper 5 Newsweek in 1989 reported that 60% of young children have blood lead levels that could impair their neurological development. Assuming a random sample from the population of all school children at risk, find: 1. The probability that at least 5 children out of 10 in a sample taken from a school may have a blood lead level that may impair development. 2. The probability you will need to test 10 children before finding a child with a blood lead level that may impair development. 3. The probability you will need to test no more than 10 children before finding a child with a blood lead level that may impair development. a. 0.9999581 b. 0.0001572864 c. 0.98976 d. 0.8337614