Find E if E = x• P(x)
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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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F893de43b-dd5b-4cce-83a1-9c933285e01c%2Ff38852b9-045f-4aff-a2d1-1f70aa0c0ddd%2Fplb6vut_processed.jpeg&w=3840&q=75)
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.

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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