Let X(1),..., X() denote the order statistics of an iid sample, X,.....X from a continuous population...

 

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Let X(1),..., X() denote the order statistics of an iid sample, X,.....X from a continuous population with edf Fx(x) and pdf fx(r). Then the pdf of X) is given by n! (j 1)!(n j)!Sx(x) [Fx (x)]~ [1 Fx(1)]* fx(x)= (a) Suppose that X,..., X, U(0, 1). Prove that X)~Beta(j,n-j+1). (b) Recall, the sample median is the number, M, such that approximately one- half of the observations are less than M and one-half are greater. Define the sample median in terms of order statistics. (c) Suppose that n = 11. What is the distribution of the sample median from the above iid sample? Let X(1),..., X() denote the order statistics of an iid sample, X,.....X from a continuous population with edf Fx(x) and pdf fx(r). Then the pdf of X) is given by n! (j 1)!(n j)!Sx(x) [Fx (x)]~ [1 Fx(1)]* fx(x)= (a) Suppose that X,..., X, U(0, 1). Prove that X)~Beta(j,n-j+1). (b) Recall, the sample median is the number, M, such that approximately one- half of the observations are less than M and one-half are greater. Define the sample median in terms of order statistics. (c) Suppose that n = 11. What is the distribution of the sample median from the above iid sample?