Let X 1 , X 2 , . . . be a sequence of independent and identically distributed random variables with distributions function F. Define Fn as follows: for any a Consider a fixed and introduce the...

Let X₁, X₂, . . . be a sequence of independent and identically distributed random variables with distributions function F. Define Fn as follows: for any a

Consider a fixed and introduce the appropriate indicator random variables (as in Section 13.4). Compute their expectation and variance and show that the law of large numbers tells us that