3-12 : Expected Value of a Game Find the expected value (or...

$3-12$ : Expected Value of a Game Find the expected value (or
expectation) of the games described.

A card is drawn from a deck. You win $\$ 104$ if the card is an
ace, $\$ 26$ if it is a face card, and $\$ 13$ if it is the eight of clubs.

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Key Concepts

Expected Value

In probability theory, the expected value is the long-term average outcome of a random process. It is calculated by summing the products of each outcome and its corresponding probability, providing a measure of the center or mean of the probability distribution.

Probability Distribution

A probability distribution describes how probabilities are assigned to each outcome of a random experiment. It is essential for determining the expected value by clearly outlining which outcomes occur and with what likelihood.

Random Variable

A random variable is a function that assigns numerical values to the outcomes of a random event, such as the monetary gain or loss in a game. It allows us to mathematically model and analyze the variability inherent in the process.

Payoffs

Payoffs represent the rewards or outcomes associated with each event in a game. In the context of expected value, each payoff is multiplied by its probability to contribute to the overall average result, reflecting the real gains or losses over many trials.

Transcript

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