Unit 6b-2

Unit 6b-2 - Chapter 7 Chapter Special Discrete...

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Chapter 7 Chapter 7 Special Discrete Distributions
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Binomial Distribution B(n,p) Binomial Distribution B(n,p) Each trial results in one of two mutually exclusive outcomes. (success/failure) There are a fixed number of trials Outcomes of different trials are independent The probability that a trial results in success is the same for all trials The binomial random variable x is defined as the number of successes out of the fixed number
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Are these binomial distributions? Are these binomial distributions? 1) Toss a coin 10 times and count the number of  heads Yes 1) Deal 10 cards from a shuffled deck and count  the number of red cards No, probability does not remain constant 1) Two parents with genes for O and A blood types  and count the number of children with blood  type O No, no fixed number
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Toss a 3 coins and count the number of Toss a 3 coins and count the number of heads heads Find the discrete probability distribution X 0 1 2 3 P(x) .125 .375 .375 .125 Out of 3 coins that are tossed, what is the probability of getting exactly 2 heads?
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Binomial Formula: Binomial Formula: ( 29 k n k p p k n k x P - - = = 1 ) ( Where: k n C k n =
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Out of 3 coins that are tossed, what is the probability of getting exactly 2 heads? ( 29 375 . 5 . 0 5 . 0 2 3 ) 2 ( 1 2 = = = x P
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The number of inaccurate gauges in a group of four is a binomial random variable. If the probability of a defect is 0.1, what is the probability that only 1 is defective? More than 1 is defective? ( 29 2916 . 9 . 0 1 . 0 1 4 ) 1 ( 3 1 = = = x P 0523 . )) 1 ( ) 0 ( ( 1 ) 1 ( = + - = P P x P
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Calculator Calculator Binomialpdf(n,p,x) – this calculates the probability of a single binomial P(x = k) Binomialcdf(n,p,x) – this calculates the cumulative probabilities from P(0) to P(k)
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Unit 6b-2 - Chapter 7 Chapter Special Discrete...

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