# Question: In this problem we formulate an alternative derivation of Equation

In this problem, we formulate an alternative derivation of Equation ( 6.58) which gives the PDF of the order statistic, Ym , which is the th largest of a sequence of random variables, X1 ,X2, XN. Start by writing Ym (y) dy = Pr(y < Ym < y + dy). Then note that Pr(y < Ym < y + dy) = Pr ({m–1 of the Xs are less than y}∩ {1 X is between y and y + dy} ∩ {n –m of the Xs are greater than y}).

Find the probability of the above event and by doing so, prove that the PDF of Ym is as given by Equation (6.58).

Find the probability of the above event and by doing so, prove that the PDF of Ym is as given by Equation (6.58).

## Answer to relevant Questions

Suppose, X, Y, and Z are independent, zero- mean, unit- variance Gaussian random variables. (a) Using the techniques outlined in Section 6.4.2, find the characteristic function of W = XY + XZ + YZ. (b) From the ...Repeat exercise 6.28 Assuming we wish to find an estimate of V given the observation U = u. (a) Find the MAP estimator of U given the observation V = v. (b) Find the ML estimator of U given the observation V= v. (c) Find ...Suppose X, Y, and Z are jointly Gaussian random variables with mean vector and covariance matrix given by Find Pr (X > 2Y – 3X). A certain system we have designed needs to be powered by a 24- V dc supply. Available to us in our lab are each of the following types of batteries whose statistical characteristics (and quantities available) are as shown in ...Prove that convergence almost everywhere implies convergencePost your question