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Probability Distributions Ch 4

Probability Distributions Ch 4 - Random variable follows a...

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Probability Distributions Random variable – variable assigned one and only one numerical value for each outcome of an experiment Discrete – Ex. Roll 1 fair die; Payout of $1 if roll is a 1, $0 if roll is 2,3,4,5, and -$1 if roll is a 6 Continuous – Ex. Weight of chips in a bag of potato chips measured in oz.
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Probability distrib applies to the population E(X) = mu = (long run average) V(X) = sigma squared = (variance = std dev squared)
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Examples Rolling fair die with payouts as given Roulette wheel and bet $2 on black
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Empirical Rule If distribution is approx bell-shaped, then 68% of outcomes 95% of outcomes 99.7% of outcomes
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Binomial Distribution
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Unformatted text preview: Random variable follows a binomial distrib if 1. Perform n identical trials 2. Only two possible outcomes (S,F) 3. P(S) is constant on each trial 4. Trials are independent 5. Random variable of interest is number of successes (S) on the n trials Binomial Calculations • Binomial formula for n trials, P(S)=p, and X is the random variable for number of S’s • P(X=x) = Where X= 0,1,2,3,…,n Table for Cumulative Binomial • Table II, textbook p.875-878 • For certain values of n and p, table gives the P(X less than or equal to x) • Example: n=6, p=.7 then P(X 4) =0.580 • What is P(X=4)? Practice Problem • Chapter 4 # 44, p. 216...
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Probability Distributions Ch 4 - Random variable follows a...

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