Need help understanding how to interpret a statistics problem

[bennyska]

Homework Statement

Let c be a constant, and define Y_{i}=1 if X_{i}\leq c and zero otherwise. Find a statistic that is a function of Y_{1},Y_{2},...Y_{n} and also unbiased for F_{X}(c)=\Phi\left(\dfrac{c-\mu}{\sigma}\right).

Homework Equations

The Attempt at a Solution

not even sure how to being. i want some function of y_1,...,y_n, call it a, such that E(a)=phi((c-mu)/sigma)... but, yeah... i have no idea where to begin.

also, sorry for my crappy latex

 

[bennyska]

oh, i left out that X_i are distributed from a N(mu,sigma), and U=SUM(X_i) and W=SUM(X_i^2), if that matters.