easy Probability
A release-checked easy problem for training Expected Value/LOTUS, Variance.
Let $X$ be a random variable with mean $\mu$ and variance $\sigma^2$, both finite. Find the constant $c$ that minimizes $f(c) = \ev{(X - c)^2}$. Report the answer when $\mu = 4$ and $\sigma^2 = 9$. If it's not possible to find such a value of $c$, report $-1$.
This Probability problem is tagged Expected Value/LOTUS, Variance. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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