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# math

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During the NCAA basketball tournament season, affectionately called March Madness, part of one team's strategy is to foul their opponent if his free-throw shooting percentage is lower than his two-point field goal percentage. Juan's free-throw shooting percentage is lower and is only 54.6% . After being fouled he gets two free-throw shots each worth one point. Calculate the expected value of the number of points Juan makes when he shoots two free-throw shots.

Aug 22, 2019

$$\text{most of this can be ignored. Two important points}\\ 1)~p = p[\text{make the free throw}] = 0.546\\ 2)~\text{n = 2, i.e. he takes two free throw shots at a time}\\ \text{The number of free throws, and thus the points he makes \\ has a binomial distribution, with the above parameters, n and p}\\ \text{it's well known that the expectation of the binomial distribution is \mu = np\\ which in this case is \mu = 2(0.546)=1.092}$$