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# MAT 121 WEEK 9 NOTES MAT 121

Syracuse

GPA 3.78

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## Popular in Probability and Statistics for the Liberal Arts I

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This 10 page Class Notes was uploaded by Aria Sivick on Sunday November 1, 2015. The Class Notes belongs to MAT 121 at Syracuse University taught by in Fall 2015. Since its upload, it has received 32 views. For similar materials see Probability and Statistics for the Liberal Arts I in Mathematics (M) at Syracuse University.

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Date Created: 11/01/15

10/26 The mean (expected value) of the probability distribution of a random variable x is The variance of the probability distribution of a random variable x is And the standard deviation is Player bets $1 on red in roulette. Let x = his net winnings. The Binomial Distributions An experiment has two outcomes, SUCCESS and FAILURE (we will count the SUCCESSES), Each time this experiment is performed, P(SUCCESS) = P, P(FAILURE) = 1- P = q. Do this n times and let x = # of SUCCESSES Arandom variable x is deﬁned ion this way is said to have a binomial distribution with parameters n and P. The possible values of x are 0,1,2,…..,n Notation: Whenever there are p and q m a stats problem, p+q = 1 q = 1 - P p + q = 1 p1 + q = 1 10/28 A2 outcome experiment with P(success) = p and P(Failure) = q = 1 - p) is performed n times and x is the number of timed success happens. Such an x has a binary probability distribution with parameters n and p. The possible values of x are 0,1,….,n. Binomial n = 5 P(success) = P What’s P(2)? P(SSFFF) = p^3, q^2 P(FFFSS) = p^3, q^2 1.)Any way of getting 2 successes has probability p^3, q^2 = p^3, q^2. 2.) There are5C2 = 10 ways to get 2 successes. 1.) SSFFF 2.) SFSFF 3.) SFFSF 4.) SFFFS 5.) FSSFF 6.) FSFSF 7.) FSFFS 8.) FFSSF 9.) FFSFS 10.) FFFSS ____ ____ ____ ____ ____ 1st 2nd 3rd 4th 5th 5C2 = 10 3.) What’s P(4)? Any way of getting 4 successes has probability p^4, q^1 And there are 5C 4= 5 ways Prob: p.p.p.p.q 1.) 2.) 3.) 4.) If x is a binomial random variable with n trials and p probability of success, then for x = 0,1,2,….,n. P(x) = nC x p^x,q^n-x Ex.) G.E. 60 - watt bubbles have a probability of failing within one year of .2 . If you have 10 such lightbulbs in your house what are the probabilities that in the next year, 1.) 4 will fail? =Ans is .88 (tableA-1) 2.) 3 will fail? =Ans is .201 3.) at least 3 will fail? P(at least 3 fail) = 1 - P(1) + P(2) = 1 - (107 + .268 + .302) = 1 - .677 = .323 Its binomial with n = 10 and p = .2 What if it was 17 light bulbs? What’s the probability n = 17, p = .2, x = 4 P(4) = 17C 4(.2)(.8) Calculator = binompdf(17, .2, 4) = .209 10/30

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