Practice question · Put in order
Order the steps for computing the expected value of a discrete random variable.
- Add all of those products together
- Read the total as the long-run average of the variable
- Attach to each value its probability from the mass function
- List every value the random variable can take
- Multiply each value by its probability
Hints
- The weights in the average are the probabilities, so they must be attached first.
- Multiplication comes before the summation.
Show the answer
- List every value the random variable can take
- Attach to each value its probability from the mass function
- Multiply each value by its probability
- Add all of those products together
- Read the total as the long-run average of the variable
Why
Expectation is a weighted sum, so every value must be paired with its own weight before anything is added. Averaging the values without weighting them is a different (and usually wrong) number, it silently assumes all outcomes are equally likely.
Practise Random Variables and Distributions
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