Homework SourseLet X1 X2 X999 be iid uniform random variables on the in
Let X1, X2, . . . , X999 be i.i.d. uniform random variables on the interval [?1/2, 1/2]. Let X(500) be the empirical median, that is X(500) = Xk for some k such that for exactly 499 indices j != k we have Xj < Xk and exactly 499 indices j != k we have Xj > Xk.
1. Find an approximation for P(X(500) > 0.01).
2. What is the probability that X(500) = X1?
Solution
![Let X1, X2, . . . , X999 be i.i.d. uniform random variables on the interval [?1/2, 1/2]. Let X(500) be the empirical median, that is X(500) = Xk for some k such](/WebImages/4/let-x1-x2-x999-be-iid-uniform-random-variables-on-the-in-980249-1761503141-0.webp "Let X1, X2, . . . , X999 be i.i.d. uniform random variables on the interval [?1/2, 1/2]. Let X(500) be the empirical median, that is X(500) = Xk for some k such")
