Exercise 1. Suppose we have a sample of values X1, X2, .-. , Xn. Let Yk…

Exercise 1. Suppose we have a sample of values X1, X2, .-. , Xn. Let Yk denote the kth order statistics of this sample. Fix p € (0,1). Write (n+1)p=r+ for a unique integer r and d e [0,1). Show the following: (i) (# of sample values s yr) = r = np+(p-O). (ii) (# of sample values > yr) = n-r= n(1- p) – p+d.