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# Let the random variable X have the pmf f(x) = (|x| + 1)2 9 , x = 1, 0, 1. Compute E(X) ISBN: 9780321923271 41

## Solution for problem 2.2-2 Chapter 2.2

Probability and Statistical Inference | 9th Edition

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Problem 2.2-2

Let the random variable X have the pmf f(x) = (|x| + 1)2 9 , x = 1, 0, 1. Compute E(X), E(X2), and E(3X2 2X + 4).

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Step 1 of 3

Section - 10.3 Modelling Linear Relationships with Randomness Present When the relationship between x and y is not deterministic, statistical procedures must be applied. For any statistical procedures, the associated formulas are valid only under speci▯c as- sumptions. The set of assumptions in simple linear regression are a mathematical description of the relationship between x and y. Such a set of assumptions is known as Model Simple Linear Regression Model: 1. For each point (x;y) in data set, the y-value is an independent observation of y = ▯ 1 + ▯ +0▯ where ▯ and1▯ are ▯0ed parameters. 2. ▯ ▯ N(0;▯ )2 3. The relationship between E(y) and x is linear: E(y) = ▯ x + ▯ 1

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Let the random variable X have the pmf f(x) = (|x| + 1)2 9 , x = 1, 0, 1. Compute E(X)