lecture06

# lecture06 - Discrete random variables Probability mass...

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Discrete random variables Probability mass function X 1 2 k p(x) p(1) p(2) p(k)

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Discrete random variables Example Roulette Straight bet: Bet \$1 on a single number x (in dollar) -1 35 p(x) Even money bet: bet \$1 on even numbers x (in dollar) -1 1 p(x)
Discrete random variables Expected value (mean, mathematical expectation) μ= E(X) = E[f(x)] = Variance ( 29 i i x p x ( 29 ( 29 i i x p x f ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 - = - = = i i x p x X E X E X V 2 2 2 μ σ

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Discrete random variables Example Roulette 1) Straight bet: Bet \$1 on a single number = 2) Even money bet: bet \$1 on even numbers μ = 2 σ = = 2 = =
Binomial Distribution tossing n coins Proportion of heads: p, Proportion of tails: q=1-p X= number of heads p(x) – the mass function p(i) = ?

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Consider tossing 4 coins possible outcomes: HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT What is the number of outcomes that have 2 heads? Binomial Distribution
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## This note was uploaded on 04/07/2008 for the course ME 314 taught by Professor Austin during the Spring '08 term at Clemson.

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lecture06 - Discrete random variables Probability mass...

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