Discrete Math › Section D · Counting › Topic D.10
Random variables and expected value
A random variable turns each outcome of an experiment into a number, and its expected value is the long-run average of that number. Linearity of expectation, combined with simple 0-or-1 variables, solves counting-flavoured problems that would be very hard to attack directly.
In this topic
- From outcomes to numbers
- Expected value
- Worked example: is the raffle worth it?
- Linearity of expectation
- Indicator variables
- Worked example: names drawn from a hat
- Worked example: shared birthdays
- Waiting times and coupon collecting
- Spread: the variance
- Common mistakes to avoid
- Key takeaways
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