Find the expected value (or expectation) of the games described.? A card is drawn from a de

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Find the expected value (or expectation) of the games...

Find the expected value (or expectation) of the games described.? $$ \begin{array}{l}{\text { A card is drawn from a deck. You win } \$ 104 \text { if the card is an }} \\ {\text { ace, } \$ 26 \text { if it is a face card, and } \$ 13 \text { if it is the } 8 \text { of clubs. }}\end{array} $$

Find the expected value (or expectation) of the games described.?
$$
\begin{array}{l}{\text { A card is drawn from a deck. You win } \$ 104 \text { if the card is an }} \\ {\text { ace, } \$ 26 \text { if it is a face card, and } \$ 13 \text { if it is the } 8 \text { of clubs. }}\end{array}
$$

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Key Concepts

Expected Value

The expected value is a fundamental concept in probability that provides a measure of the average outcome of a random experiment. It is computed by multiplying each possible outcome by its probability and then summing these products. This concept helps in understanding the long-term behavior of random processes and is used to make decisions based on probabilistic outcomes.

Discrete Random Variable

A discrete random variable is one that can take on a countable number of distinct values, each with an associated probability. In many problems, especially those modeling games or experiments with finite outcomes, the outcomes are represented by discrete random variables, which allow us to calculate parameters like the expected value and variance.

Probability Distribution

A probability distribution for a discrete random variable lists all possible outcomes and their corresponding probabilities. It provides a complete description of the stochastic behavior of the variable, allowing one to compute various statistical measures, including the expected value, and to analyze the likelihood of different outcomes in a systematic way.

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