Calculating Expected Value: A Guide to Measuring Average Outcomes in Probability and Statistics

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The expected value is a concept used in probability theory and statistics to measure the average value of a random variable

The expected value is a concept used in probability theory and statistics to measure the average value of a random variable. It represents the long-term average outcome of a random experiment or event.

To calculate the expected value of a random variable, you need to multiply each possible outcome by its corresponding probability and then sum up these products.

Let’s suppose you have a discrete random variable X with possible outcomes x₁, x₂, x₃,…, xn and their respective probabilities p₁, p₂, p₃,…, pn. The formula to calculate the expected value is:

E(X) = x₁ * p₁ + x₂ * p₂ + x₃ * p₃ + … + xn * pn

For example, let’s say you are rolling a fair six-sided die, and you want to calculate the expected value of the outcome. The possible outcomes are 1, 2, 3, 4, 5, and 6, and they all have the same probability of 1/6. Therefore, the expected value would be:

E(X) = (1 * 1/6) + (2 * 1/6) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6) = 3.5

So, the expected value of rolling a fair six-sided die is 3.5. This means that, on average, you can expect to get a value of 3.5 when rolling the die many times.

The expected value is a useful statistic as it can help make predictions and guide decision-making in uncertain situations. It provides a measure of central tendency for a random variable and can be applied in various fields, including economics, finance, and risk analysis.

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