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Find E if E = x• P(x)

Find E if E = x• P(x)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question

E=

**Title: Understanding Expected Value in Probability** **Introduction:** In probability theory, the expected value (E) of a random variable is a key concept. Here, we explore how to find the expected value given a probability distribution. **Objective:** Find \( E \) if \( E = \sum [x \cdot P(x)] \). **Explanation:** - The formula \( E = \sum [x \cdot P(x)] \) represents the expected value of a discrete random variable. - \( x \) denotes each possible value the random variable can take. - \( P(x) \) represents the probability of the random variable taking the value \( x \). - The symbol \( \sum \) (summation) indicates that you sum the product of each value and its probability across all possible values of the random variable. This formula provides a measure of the center of the distribution, essentially giving the average outcome if the experiment were repeated many times. **Applications:** Expected value is widely used in various fields, including finance, insurance, and decision-making, to predict outcomes and optimize strategies.
Transcribed Image Text:**Title: Understanding Expected Value in Probability** **Introduction:** In probability theory, the expected value (E) of a random variable is a key concept. Here, we explore how to find the expected value given a probability distribution. **Objective:** Find \( E \) if \( E = \sum [x \cdot P(x)] \). **Explanation:** - The formula \( E = \sum [x \cdot P(x)] \) represents the expected value of a discrete random variable. - \( x \) denotes each possible value the random variable can take. - \( P(x) \) represents the probability of the random variable taking the value \( x \). - The symbol \( \sum \) (summation) indicates that you sum the product of each value and its probability across all possible values of the random variable. This formula provides a measure of the center of the distribution, essentially giving the average outcome if the experiment were repeated many times. **Applications:** Expected value is widely used in various fields, including finance, insurance, and decision-making, to predict outcomes and optimize strategies.
The image contains a table that represents a probability distribution. It shows two columns: "x" and "P(x)". - The "x" column lists discrete values: - 0 - 1 - 2 - 3 - The "P(x)" column lists the probabilities associated with each "x" value: - For x = 0, P(x) = 0.157 - For x = 1, P(x) = 0.402 - For x = 2, P(x) = 0.343 - For x = 3, P(x) = 0.098 This table shows the probability of each outcome (x) occurring in a given experiment or dataset.
Transcribed Image Text:The image contains a table that represents a probability distribution. It shows two columns: "x" and "P(x)". - The "x" column lists discrete values: - 0 - 1 - 2 - 3 - The "P(x)" column lists the probabilities associated with each "x" value: - For x = 0, P(x) = 0.157 - For x = 1, P(x) = 0.402 - For x = 2, P(x) = 0.343 - For x = 3, P(x) = 0.098 This table shows the probability of each outcome (x) occurring in a given experiment or dataset.
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