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Stat400Lec6(Ch2.4,2.5)_ans

# Stat400Lec6(Ch2.4,2.5)_ans - Stet 400 [email protected] 6 Stst 400...

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Stet 400 6 Review (2.L,2.2,2.3) o Mathematical expectation (mean,variance,standard de- viation, moment) o Properties of mathematical expectation (mean,variance) o Sample mean, variance Today's Lecture (2.4, 2.5) r Bernoulli distribution and its mean, variance. r Binomial distribution and its p.m.f., properties. o Cumulative distribution function and its properties. o Geometric distribution and Negative binomial distri- bution Stst 400 Letrue 6 Bernoulli distribution Definiti,on: A random experiment is called a set of Bernoulli ;trials if it consists of several trials such that <_?vv u,t o Each tlial haronly 2 possible outcomes (usually called "Success" and "Failure") 1"1./d*rr, WTW o The probability of success p, remains constant for all trials; r The trials are independent, i.e. the event "success in trial i" does not depend on the outcome of any other trials. Examples: Repeated tossing of a fair die: success:"6", failure:"not 6". Each toss is a Bernoulli trial with P(success) : -LU Definiti,on: The random variable X is called a Bernoul- li random variable if it takes only 2 values, 0 and 1. p if r:L l-pifr:0 The p.m.f. fx("): o E(X) z oVar(X) = a G,l)t ,2 = 4 (/ EX' -Er)' (_4, = 4 ct_4) Stat 400 Lsture 6 SDritrc m12 Stat 400 Itrhrre 6 Sprinc 2012 Binomial distribution Definition: Let X be the number of successes in n inde.

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