# Question: Show that E X a 2 is minimized at a

Show that E[(X − a)2] is minimized at a = E[X].

## Answer to relevant Questions

Let X1, X2, . . . ,Xn be independent and identically distributed positive random variables. For k ≤ n, find In Example 4f, we showed that the covariance of the multinomial random variables Ni and Nj is equal to −mPiPj by expressing Ni and Nj as the sum of indicator variables. We could also have obtained that result by using the ...Consider 3 trials, each having the same probability of success. Let X denote the total number of successes in these trials. If E[X] = 1.8, what is (a) The largest possible value of P{X = 3}? (b) The smallest possible value ...Use the conditional variance formula to determine the variance of a geometric random variable X having parameter p. From past experience, a professor knows that the test score of a student taking her final examination is a random variable with mean 75. (a) Give an upper bound for the probability that a student’s test score will exceed ...Post your question