What Is Expected Value and How Is It Calculated?

TL;DR

Expected value is a calculation that determines the average of a random variable by multiplying each possible outcome by its relative frequency and summing those products. This method allows for calculating the mean even in infinite populations. Essentially, expected value is mathematically equivalent to the population mean in cases where outcome frequencies are known.

Transcript

When we first started talking about central tendencies and how we measure average, we talked about the arithmetic mean and there you just added up the numbers and you divided by the number of numbers there were. So let's say our population of numbers is-- we have a 3. Let's say we have three 3's, a 4, and a 5. That's our population. And if we wante... Read More

Key Insights

• ⚾ The population mean and expected value are closely related, but the calculation method differs based on the population size.
• 👻 The expected value allows the estimation of averages in infinite populations using relative frequencies.
• ❓ The expected value can be calculated using a probability distribution of a random variable.

Questions & Answers

Q: What is the difference between the population mean and expected value?

The population mean is calculated by adding up all the numbers in a population and dividing by the total population size. The expected value, on the other hand, is the average of a random variable in an infinite population, calculated by multiplying each outcome by its relative frequency and summing them up.

Q: Why is the expected value useful for infinite populations?

In infinite populations, it is not possible to calculate the population mean by adding up all the numbers. The expected value allows us to calculate the average by considering the relative frequencies of each outcome.

Q: How can the expected value be calculated using a probability distribution?

The expected value can be calculated by multiplying each outcome of a random variable by its probability, and summing them up. This is a way to estimate the average of the random variable in an infinite population.

Q: Can the expected value be the most probable outcome?

The expected value doesn't have to be the most probable outcome. It is a way to estimate the average of a random variable based on its relative frequencies, even if there are other outcomes with higher probabilities.

Summary & Key Takeaways

• The population mean is calculated by adding up all the numbers in a population and dividing by the total population size.

• The expected value of a random variable in an infinite population is calculated by multiplying each outcome by its relative frequency and summing them up.

• The expected value is the same as the population mean for a population with a finite size.