Question: Let Xi,j be an indicator random variable for the event that the i-th smallest number is ever compared with the j-th smallest in QuickSelect(A, k).

Let Xi,j be an indicator random variable for the event that the i-th smallest number is ever compared with the j-th smallest in QuickSelect(A, k). 

(a) Write an exact expression for E[Xi,j ]. 

(b) Show that the expected runtime of QuickSelect(A, k) is O(n).

Step by Step Solution

★★★★★

3.41 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

141 Slick analysis of QuickSort ... View full answer

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!

Q:

Let X 1 be a binomial random variable with n = 2 and pX 1 = P(success). Let X 2 be an independent binomial random variable with n = 4 and p X2 = P(success). Let X = X 1 + X 2 . Calculate if H 0 : p...

Q:

Let x be a binomial random variable with n = 20 and p = .1. a. Calculate P(x 4) using the binomial formula. b. Calculate P(x 4) using Table 1 in Appendix I. c. Use the Excel output below to...

Q:

Let A[1 n] be an array of n distinct numbers. If i A[j], then the pair (i, j) is called an inversion of A. a. List the five inversions of the array 2, 3, 8, 6, 1. b. What array with...

Q:

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...

Q:

Submitted to Management Science manuscript MS-0001-1922.65 Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title....

Q:

Microkernel operating systems aim to address perceived modularity and reliability issues in traditional "monolithic" operating systems. (i) Describe the typical architecture of a microkernel...

Q:

The Basics of Financial Mathematics Spring 2003 Richard F. Bass Department of Mathematics University of Connecticut c These notes are 2003 by Richard Bass. They may be used for personal use or class...

Q:

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...

Q:

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...

Q:

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)...

Q:

The following statement best captures Reagan's view of Welfare: Group of answer choices Welfare needs to expand as the percentage of the population that lives in poverty grows Welfare helps America...

Q:

How do the two components of this theory work together?

Q:

Caterpillars of the Monarch butterfly eat plants that are toxic to other animals so that their tissues become toxic. Birds that try to eat Monarchs vomit and then avoid the striking orange-and-black...

Q:

You have just been engaged as the external auditor for a medium-sized automotive servicing organization. The organization obtains most of its revenue in three ways: (a) it services motor-vehicle...

Q:

You are a staff information systems auditor in a public accounting firm. The firm has just acquired a new client-a small manufacturing organization. The client uses a minicomputer for its data...

Q:

The accounting department of a small company is responsible for payment of creditors. It receives a copy of each purchase order issued, a receiving document when the goods arrive, and the vendor's...

Q:

Alpha-Tech, a rapidly growing distributor of electronic components, is formulating its plans for 20x5. Carol Jones, the firms marketing director, has completed the following sales forecast....

Q:

Describe basic managerial approaches to implementing controls and how these are implemented.

Q:

The following are midterm and final examination test scores for 10 students from a calculus class, where x denotes the midterm score and y denotes the final score for each student. (a) Calculate the...

Q:

Suppose that we will receive $25 if we get two consecutive heads (H) on two flips of a balanced coin. If only one head appears, we will get $10. On the other hand, if there is no heads, we will lose...

Q:

Let X1, X2, . . ., X5 be a random sample from the normal distribution with mean 55 and variance 223. Let and (a) Find the distribution of the random variables Y and Z. (b) Are Y and Z independent?...

Q:

Dynamic random-access memory (DRAM) memory chips are made from silicon wafers in manufacturing facilities through a very complex process called wafer fabs. The wafers are routed through the fab...

Q:

Japolli Bakery tracks sales of its different bread products on a daily basis. The data for 22 consecutive days at one of its retail outlets in Nashville are in a file called Japolli Bakery ....

Q:

During the past few years, there has been a lot of discussion about the price of university textbooks. The complaints have come from many places, including students, faculty, parents, and even...