# Question

Let X1, X2… X5 be a sequence of five independent discrete random variables, each with a distribution described by:

(a) Find the probability mass function of the median (third largest) of these five samples. (b) For this random variable, is the median an unbiased estimate of the mean? That is, does the expected value of the median equal the mean of the Xi? Prove your answer.

(c) Find the variance of the median.

(a) Find the probability mass function of the median (third largest) of these five samples. (b) For this random variable, is the median an unbiased estimate of the mean? That is, does the expected value of the median equal the mean of the Xi? Prove your answer.

(c) Find the variance of the median.

## Answer to relevant Questions

A set of random variables, X1, X2, X3, Xn, are independent and each uniformly distributed over ( 0, 1). (a) Find the probability density function of Z = max(X1, X2… Xn). (b) With defined as in part (a) above, let A be ...Let be the random vector described. (a) Find the LMMSE estimator of given observation of {X2= x2, X3= x3}. (b) Find the MSE of the estimator in part (a). (c) Explain why we cannot find the MAP or ML estimators in this ...Repeat Exercise 6.37 A sequence of zero mean unit variance independent random variables, Xn, n = 0, 1, 2, …, N – 1 are input to a filter that produces an output sequence according to Xn – Xn – 1 = (Xn + Xn – 1)/ ...Let represent a three- dimensional vector of random variables that is uniformly distributed over the unit sphere. That is, (a) Find the constant c. (b) Find the marginal PDF for a subset of two of the three random ...Let Xn be a sequence of IID Gaussian random variables. Form a new sequence according to Determine which forms of convergence apply to the random sequence.Post your question

0