Expected value

High school (ages 12+)
Mathematics & Numbers

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Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/expected-value

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is Expected value known for?Law of Large Numbers demonstrates convergence of sample averages to expected value
2. What is the modern relevance?Integral to quantitative finance, actuarial science, decision theory, and machine learning algorithms
3. What is the related concepts?Variance, standard deviation, conditional expectation, risk-neutral pricing
4. How do you calculate expected value for a simple game?List each possible prize, multiply each prize by its probability, then add those numbers together. That total is the expected value.
5. Why do people use expected value in real life?It helps people decide if something is worth trying, like whether to invest money or buy insurance, because it shows the average result over many tries.

Probability Density Function (PDF): A function that describes the likelihood of a continuous random variable taking on a given value.
Law of Large Numbers: A theorem stating that as the number of trials increases, the sample average of outcomes converges to the expected value.
Stochastic Process: A process involving a sequence of random variables, often used to model systems that evolve randomly over time.