Download presentation

Presentation is loading. Please wait.

Published byHailey Drape Modified over 2 years ago

1
Probability Models The Bernoulli Family

2
Bernoulli Trials Geometric Geom(p) Mean stdev How long till first success Binomial Bion(n, p) Mean Stdev r successes given n trials The Bernoulli Family

3
What is a Bernoulli trial? Q1: do not use wikipedia! 3 characteristics: two possibilities (yes/no, true/false, success/failure) constant probability of success all events are independent or your sample is less than 10% of the population

4
Give 2 examples of a Bernoulli trial? Q2: 2 examples 3 characteristics: two possibilities (yes/no, true/false, success/failure) constant probability of success all events are independent

5
Two types of Bernoulli trials. Q3: give an example of each! Geometric: applies to waiting time situations – counting the number of trials to achieve our first success. How many components until the first success? Binomial: count the number of successes we get in a given number of trials. P(4 successes given 10 trials)

6
Skittles! Q4: is this a Bernoulli trial? Check the assumptions. The manufacturer says that there are 20% of the red ones that I like best. I jiggle my machine and one slips out. -Two outcomes: red or other -Probability of red is 20% -Getting one candy does not effect the next candy.

7
Skittles! Q5: is this a geometric or binomial? What is the probability that the first red candy is the 4 th candy selected? They are consecutive, one after the other so we are multiplying. P(red c ) P(red c ) P(red c ) P(red) (0.8)(0.8)(0.8)(0.2) = ? Or P(1 st red is the n th ) = q n-1 p Where q is the P(failure)

8
Skittles! What is the probability that the first red candy is the 4 th candy selected? This is a Geometric Probability Model Looking for the FIRST success of a Bernoulli trial Find the expected value of getting a red skittle; on average, how many do you need to select to get a red one? Create a probability model.

9
Skittles! Q6 & Q7: what is the formula for the mean and stdev of a Geom(p) model What is the probability that the first red candy is the 4 th candy selected? Find the stdev of the model Geom(p) And the stdev

10
Skittles! Q8: is this a geometric or binomial? What is the probability that the first red candy is one of the first 3 that comes out? {could be the 1 st or 2 nd or 3 rd } We are adding probabilities here. P(1 st ) + P(2 nd ) + P(3 rd ) (0.8) 0 (0.2)+(0.8) 1 (0.2)+(0.8) 2 (0.2) = ?

11
Skittles! Q9: how many different ways can you get 1 red out of 3 total? What is the probability that out of 3 candies, one will be red?.2.8

12
Skittles! What is the probability that out of 3 candies, one will be red? 3 x P(1 red) 3 x (0.8) 2 (0.2)= ?

13
Skittles! What is the probability that out of 3 candies, one will be red? This is a Binom(n, p) model Its mean or E(X) = np Its stdev or = npq

14
Skittles 3 Q10: is this a geometric or binomial? What is the probability that out of 12 candies, four will be red? {just try to do a tree out of this one! I dare you}

15
Q11: how many ways can you get 4 reds out of 12 skittles

16
Skittles 3 Q12a-e: identify n, r, p, q, and n-r What is the probability that out of 12 candies, four will be red?

17
Bernoulli Trials Geometric Geom(p) Mean stdev How long till first success Binomial Bion(n, p) Mean Stdev r successes given n trials -2 outcomes -Constant P(x) -independent The Bernoulli Family

Similar presentations

Presentation is loading. Please wait....

OK

Chapter 17: probability models

Chapter 17: probability models

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on water softening techniques dance Ppt on project financing in india Download ppt on heritage of india Ppt on hydrogen fuel cell vehicles honda Ppt on inside our earth for class 7 Types of window display ppt online Ppt on natural resources and conservation job Ppt on basic etiquettes Ppt on word association test definition Ppt on telephone etiquette training