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4-2_standev

# 4-2_standev - 4.2(cont Population Standard Deviation of a...

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4.2 (cont.) Population Standard Deviation of a Discrete Random Variable Measures how “spread out” the random variable is

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Summarizing data and probability Data Histogram measure of the  center: sample mean  x measure of spread: sample standard  deviation s Random variable Probability Histogram measure of the  center: population  mean  μ measure of spread:  population standard  deviation  σ
Example  x 0 100 p(x) 1/2 1/2 E(x) = 0(1/2) + 100(1/2) = 50  y 49 51 p(y) 1/2 1/2 E(y) = 49(1/2) + 51(1/2) = 50

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s = (X X) n - 1 2 i 2 i=1 n - Variance Variance The deviations of the outcomes from the  mean of the probability distribution   x i  -  µ σ 2  (sigma squared) is the variance of the  probability distribution Variation X - X i
s = (X X) n - 1 2 i 2 i=1 n - Variance Variance Variation σ μ 2 2 1 = ( ) ( = ) = x P X x i i i k -

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Probability Great 0.20 Good 0.40 OK 0.25 Economic Scenario Profit (\$ Millions) 5 1 -4 Lousy 0.15 10 P(X=x 4 ) X x 1 x 2 x 3 x 4 P P(X=x 1 ) P(X=x
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4-2_standev - 4.2(cont Population Standard Deviation of a...

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