Question

Calculate the expected value of $X$ for the given probability distribution. [HINT: See Quick Example 6.] $$ \begin{array}{|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 \\ \hline P(X=x) & .1 & .2 & .5 & .2 \\ \hline \end{array} $$

Name: Problem 12, Chapter 8: Finite Mathematics and Applied Calculus
Uploaded: 2021-09-15T12:20:41-08:00
Duration: 1 min 18 s
Channel: Gregory Higby
Description: Calculate the expected value of X for the given probability distribution. [HINT: See Quick Example 6.] x 1 2 3 4 P(X=x) .1 .2 .5 .2

   Calculate the expected value of $X$ for the given probability distribution. [HINT: See Quick Example 6.]
$$
\begin{array}{|c|c|c|c|c|}
\hline x & 1 & 2 & 3 & 4 \\
\hline P(X=x) & .1 & .2 & .5 & .2 \\
\hline
\end{array}
$$

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 7th Edition

Chapter 8, Problem 12

Instant Answer

Solved by Expert Gregory Higby

09/15/2021

Step 1

In mathematical terms, this is represented as E(X) = Σ [x * P(X=x)]. Show more…

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Calculate the expected value of $X$ for the given probability distribution. [HINT: See Quick Example 6.] $$ \begin{array}{|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 \\ \hline P(X=x) & .1 & .2 & .5 & .2 \\ \hline \end{array} $$

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Key Concepts

Expected Value

The expected value is a measure of the central tendency of a random variable's probability distribution. It is calculated by taking the sum of each possible value of the variable multiplied by its corresponding probability, providing a weighted average that represents the long-run average outcome of the random process.

Probability Distribution

A probability distribution assigns probabilities to each possible outcome of a random variable. In the case of a discrete random variable, this is often expressed as a probability mass function, where the sum of the probabilities of all possible outcomes is equal to one.

Discrete Random Variable

A discrete random variable is a variable that can take on a countable number of distinct values. Each value has an associated probability, and these probabilities are used to analyze the behavior of the variable, including calculating measures like the expected value.

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