Expected Value Practice

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What is Expected Value?

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The Expected Value (EV) is a calculated average of all possible outcomes of a random variable, weighted by their probabilities. It represents the long-term average if the experiment were repeated many times.

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How do you calculate Expected Value?

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To calculate the Expected Value, multiply each possible outcome by its probability and sum all these products. Formula: EV = Σ (x * P(x)) where x is the outcome and P(x) is the probability.

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What is a discrete random variable?

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A discrete random variable is one that can take on a countable number of distinct values, such as the number of customers or the number of goals scored.

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What is a continuous random variable?

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A continuous random variable can take on an infinite number of values within a given range, such as the distance traveled on a tank of gas.

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What is the difference between discrete and continuous data?

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Discrete data consists of distinct, separate values (e.g., number of students), while continuous data can take any value within a range (e.g., height, weight).

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What is the probability distribution?

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A probability distribution describes how the probabilities are distributed over the values of the random variable. It can be represented in a table, graph, or formula.

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What does it mean if a random variable has a higher expected value?

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A higher expected value indicates that, on average, the outcome is more favorable or profitable over time compared to a lower expected value.

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What is the significance of the expected value in decision-making?

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The expected value helps in making informed decisions by providing a measure of the average outcome, allowing comparisons between different options.

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How can expected value be applied in real-life scenarios?

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Expected value can be used in various fields such as finance (investments), insurance (risk assessment), and gaming (betting odds) to evaluate potential outcomes.

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What is the expected value of a fair six-sided die roll?

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The expected value of a fair six-sided die roll is 3.5, calculated as (1+2+3+4+5+6)/6.