Expected value=
The expected value is a concept in probability theory that represents the average outcome of a random variable
The expected value is a concept in probability theory that represents the average outcome of a random variable. It is calculated by multiplying each possible outcome by its probability, and then summing up these products.
Let’s break down the calculation of expected value step by step:
1. Identify the random variable:
First, we need to identify the random variable for which we want to find the expected value. This variable can represent various things, such as the outcome of rolling a dice, the number of heads obtained in a series of coin flips, or the profit from a business venture.
2. List all possible outcomes and their probabilities:
Next, we need to determine all the possible outcomes of the random variable and their respective probabilities. For example, if we are interested in the result of rolling a fair six-sided dice, the possible outcomes are the numbers 1, 2, 3, 4, 5, and 6. Since each outcome has an equal chance of occurring, the probability of each outcome is 1/6.
3. Multiply each outcome by its probability:
Now, we multiply each outcome by its corresponding probability. Using the dice example, we multiply each outcome (1, 2, 3, 4, 5, and 6) by 1/6.
4. Sum up the products:
Finally, we sum up all the products obtained from the previous step. This sum represents the expected value.
As an example, let’s calculate the expected value of rolling a fair six-sided dice:
Possible outcomes: 1, 2, 3, 4, 5, 6
Probabilities: 1/6, 1/6, 1/6, 1/6, 1/6, 1/6
Expected value = (1 * 1/6) + (2 * 1/6) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6)
Expected value = 1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6
Expected value = 21/6
Expected value = 3.5
Therefore, the expected value of rolling a fair six-sided dice is 3.5. This means that if we rolled the dice many times, the average outcome would converge to 3.5.
More Answers:
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