Question: 5. (3pt total) (a) (1pt) Find all a > 0 for which there is a finite constant ca so that the function f(x) 1

5. (3pt total) (a) (1pt) Find all a > 0 for which

5. (3pt total) (a) (1pt) Find all a > 0 for which there is a finite constant ca so that the function f(x) 1 Ca 1+ra is a probability density function. = Hint: You do not need to compute ca. For figuring out whether integrals are finite you might want to review the comparison test for improper integrals from calculus. (b) (1pt) Suppose that a > 0 is a number for which fa is a PDF. Suppose that X is a random variable with PDF fa. For which a > 0 will EX exist? (c) (1pt) Suppose that X has a PDF given by fa and X has a finite expectation. What is EX? Hint: You will not need to actually do any complicated integrations in this problem.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

In order to hedge its interest rate risk for loans starting 3 months from now, ExxonMobil's treasury department entered into a 3x5 forward rate agreement (FRA) with Barclays with a notional of $100mm...

Question: What as the average weekly safety inventory level of refined sugar from the beginning January 2022 to the end of July 2022? A. 512,465.9691 metric tons per week B. 316,002.1474 metric tons...

The study you're describing seems to be a quantitative follow-up to a previous qualitative study on the psychosocial and lifestyle impacts of Spontaneous Coronary Artery Dissection (SCAD). The study...

1. A patient takes vitamin pills daily. Each day he must have at least 240 IU of vitamin A, 5 mg of vitamin B1, and 120 mg of vitamin C. He can choose between pill 1, which contains 120 IU of vitamin...

\fPlease remember to start each question on a new page. 2. (6 points) Below are two improper integrals. If the integral is divergent, Show that it is divergent. If it is not divergent, evaluate it....

Please remember to start each question on a new page. 2. (6 points) Below are two improper integrals. If the integral is divergent, Show that it is divergent. If it is not divergent, evaluate it. (a)...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

IOE 419 Mark S. Daskin Service Operations Management IOE Department Winter, 2017 University of Michigan Problem set 4 DUE: MONDAY - February 20, 2017 Points: 100 points total Problem 1: Babette has...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

List and briefly define all quantitative measures and statistics (e.g., sample size, number of groups, number of treatments, standard deviation, standard error, mean, intercept, slope, F statistic,...

Woodinville Cement Company uses a process costing system. In 2011, the company produced and sold 100,000 bags of cement and incurred the following costs: The current selling price is $4 per unit, and...

A company with manufacturing plants located in Massachusetts and Virginia has labor-hour and wage requirements for the manufacture of three inflatable boats as given in the following two tables: Let...

Evaluate the double integral R f ( r , ) d A . 0 2 0 7 r e - r 2 d r d

The motor A accelerates uniformly from zero to 3600 rev/min in 8 seconds after it is turned on at time t = 0. It drives a fan (not shown) which is attached to drum B. The effective pulley radii are...

In problem use the Laplace transform to solve the given initial-value problem. Use the table of Laplace transforms in Appendix III as needed. y'' + y = f(t), y(0) = 1, y'(0) = 0, where Appendix III...

Assume that Sarazan SA has a shareoption plan for top management. Each share option represents the right to purchase a R$1 par value ordinary share in the future at a price equal to the fair value of...

A fenced enclosure consists of a rectangle of length L and width 2R, and a semicircle of radius R, as shown in Figure P20. The enclosure is to be built to have an area A of 1600 ft 2 . The cost of...

A fenced enclosure consists of a rectangle of length L and width 2R and a semicircle of radius R, as shown in Figure P13. The enclosure is to be built to have an area A of 2000 ft 2 . The cost of the...

Determine if the overhead allocated to the product relates to a single plantwide overhead rate method, multiple production department factory overhead rate method, or activity-based costing...

35. Satellites are launched according to a Poisson process with rate . Each satellite will, independently, orbit the earth for a random time having distribution F. Let X(t) denote the number of...

39. A system consists of two independent machines that each functions for an exponential time with rate . There is a single repairperson. If the repairperson is idle when a machine fails, then repair...

36. Each of n skiers continually, and independently, climbs up and then skis down a particular slope. The time it takes skier i to climb up has distribution Fi, and it is independent of her time to...