{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

08 Discrete Probability Distributions Part 2

# 3-4 3 2.6*4*3)4.1(4.13221==-=)1(xp1515binomial

This preview shows pages 14–23. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 3--4 3 2.6.*4.*3)4.1(4.13221==-=)1(XP1515Binomial distribution: Example1535% of all voters support Proposition A. If a random sample of 10 voters is polled, what is the probability that exactly three of them support the proposition?1616Binomial distribution: Example1635% of all voters support Proposition A. If a random sample of 10 voters is polled, what is the probability that exactly three of them support the proposition?i.e., find P(x= 3) if n= 10 and p= 0.35There is a 25.22% chance that 3 out of the 10 voters will support Proposition A..2522(0.65)(0.35)3!7!10!qpx)!(nx!n!3)P(x73xnx==-==-17Binomial distribution in Excel: X ~ Binomial (n, p)17=BINOMDIST( x , n, p, 0/FALSE)=BINOMDIST( x , n, p, 1/TRUE)X ~ Binomial (n = 10, p = 0.35)P(X = 3)P(X ≤ 3) (= P(X=0) + P(X=1) + P(X=2) + P(X=3))xnxppxnxXPxP--===)1()()(inixippinxFxXP-=-==≤∑)1()()(1818Binomial example: Alumni pledge solicitor18Sarah is working in the Drexel Alumni Association, calling up alum and soliciting funds for a new scholarship program. Suppose the probability that Sarah wins a pledge for funds from a randomly chosen target alum is 1/4. If she calls 8 alums this evening, what is the probability that:1.No money will be pledged?2.Exactly two pledges will be made?Binomial (n=8, p=0.25)P(X=2) = BINOMDIST(2,8,0.25,0) = 0.31151001.75.25.8)(8===XP1919Binomial example: Alumni pledge solicitor193.At least two pledges will be made?4.Sarah is paid \$6.00 per hour for this job and makes 8 calls per hour. Suppose she gets a bonus of \$5.00 for each successful call. What is her expected earning per hour?P(X≥2) = 1 – P(X≤1) = 1 – BINOMDIST(1,8,0.25,1)= 0.6329E[X] = np = 2E[bonus] = 5*E[X] = 10Hourly pay = 6Exp hourly earning = 1620In Binomial distribution, each trial is independent and identical. (Sampling with replacement)If we draw n candies one at a time (out of N total), depending on what candies are drawn already, the probability that a particular candy is drawn next changes. (Sampling without replacement)Does the number of successes out of n follow a binomial? (Yes or No). As the size of the total candy pool (N) increases, Sampling without replacement converges to sampling with replacementBinomial distribution: Caveat (Effect of finite population)21Discrete random variable: Poisson distribution Poisson distribution: Used to count the number of occurrences of a particular event during an interval of time or over a space For example: The number of customer arrivals in an hourThe number of calls received at a call center in a two-hour shiftThe number of defects on a 17 inch LCD screen22Poisson distribution Properties and assumptions of the poisson distributionCan take any non-negative integervalue (x=0,1,2,3,…….):the average number of outcomes of interest per unit time segment or unit space segment....
View Full Document

{[ snackBarMessage ]}

### Page14 / 28

3-4 3 2.6*4*3)4.1(4.13221==-=)1(XP1515Binomial distribution...

This preview shows document pages 14 - 23. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online