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Lesson 6 Math Expectation - Mathematical Expectation...

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Mathematical Expectation Definition: Mean or Expected Value Let X be a random variable with probability distribution f(x). The mean or expected value of X is for X a discrete random variable and for X a continuous random variable. Example: 1. The probability distribution of the discrete random variable X is for x = 0, 1, 2, 3. Find the mean of X. = = x x xf X E ) ( ) ( μ - = = dx x xf X E ) ( ) ( μ x x x x f - = 3 4 3 4 1 3 ) (
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Examples 1. In a gambling game a man is paid P10 if he gets all heads or all tails when three coins are tossed, and he will pay out P4 if either one or two tails show. What is his expected gain? 2. By investing in a particular stock, a person can make a profit in one year of $4000 with probability 0.3 or take a loss of $1000 with probability 0.7. What is the person’s expected gain? 3. If a dealer’s profit, in units of $5000, on a new automobile can be looked as a random variable X having the density function Find the average profit per automobile.
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