Random variables with common distribution function

Reference no: EM13985355

1. The statistician Piggy has to wait an amount of time T0 at the post office on an occasion when she is in a great hurry. In order to investigate whether or not chance makes her wait particularly long when she is in a hurry, she checks how many visits she makes to the post office until she has to wait longer than the first time. Formally, let T1, T2, . . . be the successive waiting times and N be the number of times until some Tk > T0, that is, {N = k} = {Tj ≤ T0, 1 ≤ j k, Tk > T0}. What is the distribution of N under the assumption that {Tn, n ≥ 0} are i.i.d. continuous random variables? What can be said about E N ?

2. Let X1, X2, . . . , Xn be independent, continuous random variables with common distribution function F(x), and consider the order statistic (X(1), X(2), . . . , X(n)). Compute E(F (X(n)) - F (X(1))).

Reference no: EM13985355

Questions Cloud

Problem regarding the distributed random variables : 1. Let X1, X2, X3, and X4 be independent, U (0, 1)-distributed random variables. Compute

Plot the number of simplex iterations : Plot the number of simplex iterations (y) versus the number of constraints (m). Save your plot as a picture file, and upload it in your discussion thread.

Calculate the magnitude of the magnetic field : The electric field strength in the selector is 4.819 x 105 N/C. The atom passes straight through the selector without any deflection of its path. From the information above, determine the magnitude of the magnetic field, BI.

One very important decision that marketers : One very important decision that marketers need to make is which channel of distribution to use for its products or services. Four primary considerations need to be analyzed before making the distribution choice: 1) Distribution coverage required; 2)..

Random variables with common distribution function : Let X1, X2, . . . , Xn be independent, continuous random variables with common distribution function F(x), and consider the order statistic (X(1), X(2), . . . , X(n)). Compute E(F (X(n)) - F (X(1))).

Discuss the six forms of deferred compensation : Discuss the six forms of deferred (stock) compensation. List and discuss four possible limitations of merit pay programs. Please discuss in detail and provide examples for each of the limitations

Determine the expected value of the length : Two points are chosen uniformly and independently on the perimeter of a circle of radius 1. This divides the perimeter into two pieces. Determine the expected value of the length of the shorter piece.

Is there really any bargaining over such terms : College of Business, Frank Bean, removed Littleton's responsibilities for advising graduate students and scheduled him for undergraduate courses for the next semester. Littleton filed suit in a federal district court against Bean, the university, ..

Thousands of airports around the world : There are thousands of airports around the world. Some are better than others. Whether you are comparing on-time takeoffs, baggage handling, signage, concessions, etc., there are certain things we can recall as our best and worst airports.

User Account

All Pages