Question: Let X1,..., X,, be i.i.d. random variables with a continuous cdf F(x). Define the random variables Y1,..., Yn by { 1, if X; >

Let X1,..., X,, be i.i.d. random variables with a continuous cdf F(x).

Let X1,..., X,, be i.i.d. random variables with a continuous cdf F(x). Define the random variables Y1,..., Yn by { 1, if X; > c 0, if X; < c, Y; = where c is a constant and i = 1,..., n. Find the distribution of Y = E Y;. i=1

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