61.Two Hundred Coins in a Box
★★★expected valueJane Street
Two hundred fair coins are flipped and is the number of heads that come up. A box is then filled with dollars, where a negative amount means you owe that much instead. What is the expected amount of money in the box?
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The expectation of squared is not the square of the expectation of , and the gap between them is exactly the variance. Check what the number of coins is doing against the 100 sitting inside the formula.
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