Problem 5.10.10
Suppose you have n suitcases and suitcase i holds Xi dollars where X1, X2, …, Xn are iid continuous uniform (0, m) random variables. (Think of a number like one million for the symbol m.) Unfortunately, you don’t know Xi until you open suitcase i.
Suppose you can open the suitcases one by one, starting with suitcase n and going down to suitcase 1. After opening suitcase i, you can either accept or reject Xi dollars. If you accept suitcase i, the game ends. If you reject, then you get to choose only from the still unopened suitcases.
What should you do? Perhaps it is not so obvious? In fact, you can decide before the game on a policy, a set of rules to follow. We will specify a policy by a vector (t1, … tn) of threshold parameters.
Problem 5.10.10 Suppose you have n suitcases and suitcase i holds Xi dollars where X1, X2, …, Xn ...
Problem 5.10.10 Suppose you have n suitcases and suitcase i holds Xi dollars where X1, X2, …, Xn are iid continuous uniform (0, m) random variables. (Think of a number like one million for the symbol m.) Unfortunately, you don’t know Xi until you open suitcase i. Suppose you can open the suitcases one by one, starting with suitcase n and going down to suitcase 1. After opening suitcase i, you can either accept or reject Xi dollars. If...
this question is from the book Probability and Stochastic Processes (3rd Edition) by Yates question 5.10.10 2. Problem 5.10.10 Suppose you have n suitcases and suitcase i holds I dollars where Xi. X. I are iid continuous uniform (0. m) random variables. Think of mber ke one milion for the symbo m.) Unfortunately, you don t know X, until you open suitcase Suppose you can open the suitcases one by one, starting with suitcase n and going down to suitcase...
Suppose n numbers X1, X2, . . . , Xn are chosen from a uniform distribution on [0, 10]. We say that there is an increase at i if Xi < Xi+1. Let I be the number of increases. Find E[I].
Problem 4 Suppose X1, ..., Xn ~ f(x) independently. Let u = E(Xi) and o2 = Var(Xi). Let X Xi/n. (1) Calculate E(X) and Var(X) (2) Explain that X -> u as n -> co. What is the shape of the density of X? (3) Let XiBernoulli(p), calculate u and a2 in terms of p. (4) Continue from (3), explain that X is the frequency of heads. Calculate E(X) and Var(X). Explain that X -> p. What is the shape...
Suppose that Xi, X2,..., Xn are independent random variables (not iid) with densities x, (x^, where 6, > 0, for i-1, 2, , n. versus H1: not Ho (c) Suppose Ho is true so that the common distribution of X1, X2,..., Xn, now viewed as being conditional on 6, is described by where θ > 0. Identify a conjugate prior for 0. Specify any hyperparameters in your prior (pick values for fun if you want). Show how to carry out...
σ2). 6. Suppose X1, Yİ, X2, Y2, , Xn, Y, are independent rv's with Xi and Y both N(μ, All parameters μί, 1-1, ,n, and σ2 are unknown. For example, Xi and Yi muay be repeated measurements on a laboratory specimen from the ith individual, with μί representing the amount of some antigen in the specimen; the measuring instrument is inaccurate, with normally distributed errors with constant variability. Let Z, X/V2. (a) Consider the estimate σ2- (b) Show that the...
Need help solving a linear programming problem. Can you please use step by teps in excel solver and show work so I can follow. Thank you. Portfolio Xi= The amount of dollars to invest in stock i i=1=A, 2=B, 3=C, 4=D, 5=E Max Expected Return Z=4.5X1+5.2X2+6.0X3+7.2X4+4.2X5 Subject to: X1+X3<=50,000 X2+X5<=50,000 X4<=50,000 X1>=20,000 X3<=0.2(X1+X3) X1+X2+X3+x4+X5<=100,000 Xi>=0 for all i
Suppose that X1, X2, ..., Xn are independent random variables (not iid) with densities ÍXi(z10,) -.2 e _ θ:/z1(z > 0), where θί 〉 0, for i = 1, 2, , n. (a) Derive the form of the likelihood ratio test (LRT) statistic for testing versuS H1: not Ho. You do not have to find the distribution of the likelihood ratio test (LRT) statistic under Ho- Just find the form of the statistic. (b) From your result in part (a),...
3. [20 marks] Consider the multinomial distribution with 3 categories, where the random variables Xi, X2 and X3 have the joint probability function where x = (zi, 2 2:23), θ = (θί, θ2), n = x1 + 2 2 + x3, θι, θ2 > 0 and 1-0,-26, > 0. (a) [4 marks] Find the maximum likelihood estimator θ of θ. (b) [4 marks] Find that the Fisher information matrix I(0) (c) [4 marks] Show that θ is an MVUE. (d)...
4. Setup: Suppose you have observations X1,X2,X3,X4,X5 which are i.i.d. draws from a Gaussian distribution with unknown mean μ and unknown variance σ2. Given Facts: You are given the following: 15∑i=15Xi=0.90,15∑i=15X2i=1.31 Bookmark this page Setup: Suppose you have observations X1, X2, X3, X4, X5 which are i.i.d. draws from a Gaussian distribution with unknown mean u and unknown variance o? Given Facts: You are given the following: x=030, =1:1 Choose a test 1 point possible (graded, results hidden) To test...