probdist_s08_bw_p1

probdist_s08_bw_p1 - Stat-Bus 127 Probability Distributions...

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Stat-Bus 127 Probability Distributions Dr. Linda M. Penas Spring 2008 1 Probability Distributions (p. 27) DEFN : random variable: variable that takes on different values depending on chance. Probability Distributions (p. 27) EXAMPLE : Roll a die. Let X = # on the face that appears. The X is a random variable that can take on values 1,2,3,4,5,6 More definitions DEFN : discrete random variable is an r.v. for which there exists a discrete set of values with nonzero probability; a random variable whose range space (or # of possible outcomes) is either finite or countably infinite; integer-valued. DEFN : continuous random variable :is±a± random variable whose values form a continuum, i.e., an infinite number of values that can be put into a 1-1 correspondence with the real numbers. Probability Dist. Functions DEFN : Probability distribution function : function that describes the behavior of a random variable (must be non-negative) Discrete Prob. Distribution DEFN : A probability mass function (pmf), or discrete probability distribution , is a mathematical relationship,p(x),that assigns to any value x of a discrete r.v. X the probability P(X = x). Discrete Prob. Distribution NOTE : p(x) is a p.m.f. iff (if and only if) ( ) ( ) 0 for all ip x x () = 1 x ii p x

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Stat-Bus 127 Probability Distributions Dr. Linda M. Penas Spring 2008 2 Cumulative Dist. Function DEFN : The cumulative distribution function , (cdf) for a discrete r.v. X is given by F(x) = P(X x) = ( ) i i xx px NOTES about cdf 0 F(x) 1 lim F(x) = 0 x →−∞ lim F(x) = 1 x →∞ (If a F(x) < b, is nondecr then F(a e ) asing. F ) (b) Your Task Read pages 27 – 31 Go to page 32 BINOMIAL DISTRIBUTION (p. 32) An experiment often consists of repeated trials, each of which can result in one of two possible outcomes, either success or failure . EXAMPLE : Testing assembly line items, vaccines, etc. “Success” vs “Failure” ¾ A manufacturing plant labels items as either “defective” or “acceptable” ¾ A firm bidding for a contract will either “get the contract” or “not get the contract” ¾ A marketing research firm receives survey responses of “yes I will buy” or “no I will not” ¾ New job applicants either “accept the offer” or “reject the offer” Binomial Experiment Characteristics of the Binomial Experiment : ¾ A trial has only two possible outcomes – “success” or “failure” ¾ Fixed number, n, of independent identical trials ¾ Probability of a success, p, remains constant from trial to trial ¾ q = (1-p) = is the probability of a failure
Stat-Bus 127 Probability Distributions Dr. Linda M. Penas Spring 2008 3 Example : A coin is tossed three times and the number of heads recorded. Is this a binomial experiment? SOLN : Yes since there are 3 independent repeated trials; success = {h}, failure = {t}, p remains constant (= ½ if balanced) EXAMPLE : Lots of 40 components each are called acceptable if they contain no more than 3 defectives. The procedure for sampling is to select 5 components, without replacement, at random and to reject the lot if a defective is found. Is this a binomial experiment?

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This note was uploaded on 04/21/2008 for the course BUS 127 taught by Professor Penas during the Spring '08 term at UC Riverside.

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probdist_s08_bw_p1 - Stat-Bus 127 Probability Distributions...

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