Example class 9

# Example class 9 - The University of Hong Kong Department of...

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The University of Hong Kong Department of Statistics and Actuarial Science STAT1301 Probability and Statistics I Example class 9 Expected Values I. The Expected Value of a Random Variable (a) If X is a discrete random variable with frequency function p(x), the expected value of X, denoted by E(X), is (b) If X is a continuous random variable with density f(x), then E(X) is also referred to as the mean of X and is often denoted by μ . II. Variance and Standard Deviation The standard deviation is an indication of how dispersed the probability distribution is about its center, or about its expectation. (a) If X is discrete random variable with frequency function p(x) and expected value μ =E(X), (b) If X is continuous random variable with density function f(x) and E(X) = μ . Theorem A III. Linear Combinations of Random Variables i. ii. Exercise 1. Suppose E(X) = expected value of X, prove the Theorem 1

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2. An actuary is designing a new game for a casino. The player of the new game pays \$1
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Example class 9 - The University of Hong Kong Department of...

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