Question: 7. If X is a positive integer valued random variable, with mass function , , then the function is called the (discrete) hazard rate function

7. If X is a positive integer valued random variable, with mass function , , then the function is called the (discrete) hazard rate function of X.

(a) Express in terms of the values .

(b) If is increasing (decreasing) in i then the random variable X is said to have increasing (decreasing) failure rate. Let be a random variable whose distribution is that of the conditional distribution of given that . That is, Show that if X has increasing (decreasing) failure rate it and only if stochastically decreases (increases) in n.

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 Introduction To Probability Statistics Questions!

If X is a positive integer valued random variable, with mass function pi = P(X = i), i 1, then the function (i) = P(X = i|X i) is called the (discrete) hazard rate function of X. (a) Express P(X...

Korea Advanced Institute of Science and Technology Department of Electrical Engineering & Computer Science EE531 Statistical Learning Theory, Spring 2016 Assignment I Issued: Mar. 19, 2016 Due: Apr....

14. The Discrete Hazard Rate Method: Let X denote a nonnegative integer valued random variable. The function (n) = P{X = n | X n}, n 0, is called the discrete hazard rate function. (a) Show that P{X...

14. The Discrete Hazard Rate Method: Let X denote a nonnegative integer valued random variable. The function , is called the discrete hazard rate function. (a) Show that . (b) Show that we can...

The Discrete Hazard Rate Method: Let X denote a nonnegative integer valued random variable. The function (n) = P{X = n|X n},n 0, is called the discrete hazard rate function. (a) Show that P{X = n}...

14. The Discrete Hazard Rate Method: Let X denote a nonnegative integer valued random variable. The function () = P[X = n\X> n], > 0, is called the discrete hazard rate function. (a) Show that P{X =...

QUESTION 1 The definition of a variable outside any function is called local variable definition global variable definition global function definition global function header QUESTION 2 A void...

In this question you will be asked to reflect on a project you have been involved in or observed, in which a design evolved, or could have evolved, through applying a theory of user behaviour. You...

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

Consider the trigonometric series a0 2 + X r=1 (ar cos rx + br sin rx) where a0, a1, a2, . . . and b1, b2, . . . are constants and suppose that f(x) is a periodic function of x with period 2. (a)...

Write a JavaFX application - CircleOverlap.java- that presents 20 circles (use the JavaFX Circleclass), each with a random radius and location. If a circle does not overlap any other circle, fill the...

Christy is developing a business plan for a dog grooming service. Her service would provide fur dying, claw trimming, facials, massage, etc. The monthly rent for the grooming space would be $750 and...

For a month's sales, sales are made on credit. 3 2 % pay in the month of the sale and 3 2 % are collected in the month following the sale 3 1 % is collected two months after the sale. The balance is...

a. Find the open intervals on which the function is increasing and decreasing. b. Identify the functions local and absolute extreme values, if any, saying where they occur. (u) = 3 2 - 4 3

41. Carloads of customers arrive at a single-server station in accordance with a Poisson process with rate 4 per hour. The service times are exponentially distributed with rate 20 per hour. If each...

42. In the two-class priority queueing model of Section 8.6.2, what is WQ? Show that WQ is less than it would be under FIFO if E[S1] E[S2].

43. In a two-class priority queueing model suppose that a cost of Ci per unit time is incurred for each type i customer that waits in queue, i = 1, 2. Show that type 1 customers should be given...

Using the data below for the Ace Guitar Company Sales Region Region $666,000 $814,000 Cost of goods sold 253,100 309,300 Selling expenses 159,800 195,400 Service department expenses Purchasing...

12 of 13 View Policies Current Attempt in Progress - / 3.33 A= Preferred stock has contractual provisions that give it a preference over common stock as to and to dividends in the event of...

Rundle Company makes and sells lawn mowers for which it currently makes the engines. It has an opportunity to purchase the engines from a reliable manufacturer. The annual costs of making the engines...