Worksheet 15: Expected Value#
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Calculate the expected number of minutes we’ll spend at the airport using strategy 2.
With probability \(1 - \frac{1}{5}\), we make our flight, and spend only \(45\) minutes at the airport.
With probability \(\frac{1}{5}\), we miss our flight, and spend \(240\) minutes at the airport.
\(\mathbb{E}[M] = \sum_{m} m \cdot \Pr[M = m]\), where the sum is over all possible values \(m\) that \(M\) takes.
If my brother takes 100 flights, what is the expected number of flights he misses?
Roulette. The roulette wheel has 38 numbers, 18 of which are red. Let \(W\) be the amount of money you win if you place $ 1 on red.
a. What is \(\mathbb{E}[W]\)?
b. Is it worth it to bet on red in roulette?
Consider the following simple coinflip game:
You flip a fair coin.
If it lands on heads, you get $300.
If it lands on tails, you get nothing.
a. How much would you be willing to pay in order to play this game? It may be helpful to calculate the expected value of your earnings.
b. Does anything change if you can play it an unlimited number of times?