14111cn8.7-8

# 14111cn8.7-8 - • ¯ x is the expected value(mean • σ x...

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c ± Kendra Kilmer October 27, 2011 Section 8.3 - Variance and Standard Deviation Example 1: Draw the histograms for the random variables X and Y that have the following probability distribu- tions: x P ( X = x ) 1 . 1 2 . 1 3 . 6 4 . 1 5 . 1 y P ( Y = y ) 1 . 3 2 . 1 3 . 2 4 . 1 5 . 3 Deﬁnition : Suppose a random variable X has the following probability distribution: x P ( X = x ) x 1 p 1 x 2 p 2 · · · · · · x n p n and expected value E ( X ) = μ . Then the variance of the random variable X is Var( X )= p 1 ( x 1 - μ ) 2 + p 2 ( x 2 - μ ) 2 + ··· + p n ( x n - μ ) 2 . Deﬁnition : The standard deviation of a random variable X , σ , is deﬁned by: σ = p Var ( X ) 7

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c ± Kendra Kilmer October 27, 2011 Finding expected value and standard deviation using the calculator: Enter the x-values into L1 and the corresponding probabilities into L2 (STAT 1:Edit) On the homescreen type 1-Var Stats L 1 , L 2 (STAT CALC 1:1-Var Stats)
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Unformatted text preview: • ¯ x is the expected value (mean) • σ x is the standard deviation • To ﬁnd variance, you would need to recall that Var ( X ) = σ 2 Example 2 : Referring to Example 1, a) Find the variance and standard deviation of X . b) Find the variance and standard deviation of Y . Example 3: The percent of the voting age population who cast ballots in presidential election years from 1980 through 2000 are given below: Election Year 1980 1984 1988 1992 1996 2000 Turnout Percentage 53 53 50 55 49 51 Find the mean and standard deviation of the voter turnout. Section 8.3 Highly Suggested Homework Problems: 3, 5, 7, 9, 11, 13, 15, 22 8...
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14111cn8.7-8 - • ¯ x is the expected value(mean • σ x...

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