Explain what is expected value and how is it calculated
The expected value is a concept in probability theory that represents the average outcome of a random variable over a large number of trials or events. It is used to estimate what the future value might be based on the probability of various outcomes.
To calculate the expected value, you need to multiply each possible outcome by its respective probability and then sum up these products. Let's break down the steps:
1. Identify the possible outcomes: First, you need to identify all the possible outcomes of the random variable in question. For example, if you are flipping a fair coin, the possible outcomes can be either heads or tails.
2. Assign probabilities to each outcome: Next, you need to determine the probability associated with each outcome. In the case of a fair coin flip, the probability of getting heads or tails is 0.5 for each.
3. Multiply each outcome by its respective probability: Multiply each outcome by its probability. For example, if you assign 1 to heads and 0 to tails, you would multiply 1 by 0.5 and 0 by 0.5.
4. Sum up the products: Finally, sum up the products obtained from step 3. In the coin flip example, it would be (1 * 0.5) + (0 * 0.5) = 0.5.
Therefore, the expected value in this case would be 0.5, indicating that on average, you can expect to get 0.5 heads in one fair coin flip.