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Section 7.2

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Mean of a probability distribution is the long- run average outcome, µ, or µ x. Also called the expected value of x, or E(X). µ x = x i P i Example: X heads in four coin tosses. Find the mean of X. Xi01234Xi01234 P i.0625.25.375.25.0625

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Inhabitants: 1 2 3 4 5 6 7 Proportion:.25.32.17.15.07.03.01 Find mean household size.

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In a sample that uses mean x to estimate the value of the population mean µ, as the # of observations increases, mean x eventually approaches mean µ.

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1. If X is a random variable and a and b are fixed numbers, then: µ a+bx = a + bµ x 2. If X and Y are random variables, then: µ X+Y = µ X + µ Y Example: Dan (X) and Danna (Y) are on a math team. Each takes 10 tests on a variety of concepts. Their scores are then combined and averaged for the team score. µ X = 82 µ Y = 86 Find the mean score of the team, µ X+Y

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σ x 2 Variance of random variable X: σ x 2 = (x i - µ X ) 2 p i Example: Given the following distribution, find the mean and standard deviation: Units Sold 1000 3000 5000 10,000 Probability.1.3.4.2

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1. If X is a random variable and a and b are fixed numbers, then σ 2 a+bx = b 2 σ x 2 2. If X and Y are independent random variables, then σ 2 x+y = σ x 2 + σ y 2 σ 2 x-y = σ x 2 + σ y 2 3. What about standard deviation?

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Two golf players, Jake(X) and Carrine(Y), have the following stats: µ x = 110, σ x = 10 µ y = 100, σ y = 8 Find the difference in their mean scores. Find the variance of the difference between their scores. Find the standard deviation of the difference in their scores.

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Binomial distribution Nutan S. Mishra Department of Mathematics and Statistics University of South Alabama.

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