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After you finish the circle, read through your measurement records and find the lowest measurement. The gas can position corresponding to the lowest measurement should be your starting position if the car has no gas initially. It may take some thinking to fully understand this argument.

I'd recommend that you again draw a figure and give this argument some careful thoughts if you don't find the reasoning obvious. In a proof by contradiction or indirect proof, you show that if a proposition were false, then some logical contradiction or absurdity would follow.

Thus, the proposition must be true. Can you prove that J2 is an irrational number? A rational number is a number that can be expressed as a ratio of two integers; otherwise it is irrational. As shown.

F' - n, then the same statement also holds for III tgure 2. Li s Xi' It can reach x. This is a classical example of proof by contradiction. If J2 is not an irrational it can be expressed as a ratio of two integers m and n.

If m and n have any factor, we can remove it by dividing both m and n by the common factor. So in we will have a pair of m and n that have no common factors. It is called. Let's express m as Zx, where x is an 2. But that both m and n are even contradicts the earlier statement 2. Rainbow hats Seven prisoners are given the chance to be set free tomorrow. An executioner will put a hat on each prisoner's head. Each hat can be one of the seven colors of the rainbow and the hat colors are assigned completely at the executioner's discretion.

Every prisoner can They cannot communicate with others in any form, or else they are immediately executed. Then each prisoner writes down his guess of his own hat color. If at least one prisoner correctly guesses the color of his hat, they all will be set free immediately; otherwise they will be executed. They are given the night to come up with a strategy. Is there a strategy that they can guarantee that they will be set free?

In the previous prisoner problem, the prisoners can hear others' guesses. So one prisoner's declaration gives all the necessary information other prisoners need. In this problem, prisoners won't know what others' guesses are. To solve the problem, it does require an aha moment. The key to the aha moment is given by the hint. Once you realize that if we code the colors to ,. Then each prisoner i-let's label them as 0. Chapter 3 Calculus and Linear Algebra Calculus and linear algebra lay the foundation for many advanced math topics used in quantitative finance.

Since most of the tested calculus and linear algebra. If your memory of calculus or lmear algebra IS a little rusty, spend some time reviewing your college textbooks! Neither is it my intention to do so. And unless necessary, it does so. Basics of derivatives Let's begin with some basic definitions and equations used in lim. Although the notations may be different, you can find these materials III any calculus textbook. Local maximum or minimum: suppose that J x is differentiable at c and is defined on an open interval containing c.

If J c is either a local maximum value or a local. Solution: This is a good problem to test. To derive d ln lnx. At point x c, if. Is it true? That depends on whether J x lnx is an increasing or decreasing function x. Taking the derivative of lex , we have J x 1 x: x2 ' c. Alternative approach: If you are familiar with the Taylor's series, which we will discuss 1 Although there are derivative functions for all trigonometric. The rest can be derived using the product rule or the quotient rule.

For dx example,. Again, let's begin with some basic definitions. If we can find a fu. What is ::c wilt ra flUS 1. Solution: This problem is an a licati fi. For these '. ICU t part IS to correctly [annulate the integration. The general IntegratIOn function to calculate 3D vol. Figure 3. If you cut the i. An alternative app h " ". IS lllscnbed inside both cylinders. Let's imagine a sphere that lt sphere should have a radius of A IS mscribed inside the intersection as well.

The from the sphere IS "" Inscribed r iine. L V 4 Intersect,OJ! The snow began to fall some time before noon at a constant. The plow removed snow at a constant volume per minute. At I pm, it had moved 2 miles and at 2 pm, 3 miles. When did the snow begin to fall? Solution: Let's denote noon as time 0 and assume snow began to fall T hours before noon. Overall, this question, although fairly straightforward, tests analytical skills, integration knowledge and algebra knowledge.

In Chapter 4, we will demonstrate its value in probability and statistics. Here we just use one example to show its application:. By definition, we have. Tthe integration in a. The general chain rule' Supp th. If you've forgotten the pdf of the standard normal distribution or if you are specifically asked to prove.

IJ'''''' x -I for all i between xo' and x, we get constraint. Applying Taylor's series, we have. If Taylor's series does not jump to your mind, the condition that n is an integer may give you the hint that you can try the induction method. Alternatively, we can use algebra since it is obvious that the solution should be slightly higher than 6.

Could you explain some root-finding algorithms to solve f x a differentiable function. Convergence of Newton's meth d. If you do not remember Newton's meth d. Bisection method is an intuitive root-finding algorithm. Since I x is differentiable, there must be an x between Go and bo that makes f x.

Solution: Besides Newton's method. Similar to Newton's method, convergence is not guaranteed if initial values are not close to the root. Solution: The distance D from th " I'. Mathematically, the problem can be expressed as.

Solution: Unlike the last example, this equation is not separable in its current form. But we can use a change of variable to turn it into a separable differential equation. A homogenous linear '. It is easy to verify that the general solutions indeed satisfy the homogeneous solutions by taking the first and secondary derivatives of the general solutions.

SO the solution to There are 3 random variables x, y and z. The correlation between x and y is 0. What is the maximum and minimum correlation. Solution: We can consider random variables x, y and z as vectors. Similarly the angle between x and z is. For Y and z to have the maximum correlation, the angle between them needs to be the smallest. In this case, the minimum angle is 0 when vector y and z are in the same direction and the correlation is 1. For the minimum correlation, we want the maximum angle betweeny and z, which is the case shown in Figure 3.

If you still remember all you need is that. It can represent the coordinates of uc I ean space. Open navigation menu. Close suggestions Search Search. User Settings. Skip carousel. Carousel Previous. Carousel Next. What is Scribd? Uploaded by Mike Pandey. Document Information click to expand document information Original Title [Xinfeng Zhou]A practical Guide to quantitative finance interviews.

Did you find this document useful? Is this content inappropriate? Report this Document. Flag for inappropriate content. Download now. For Later. Related titles. Carousel Previous Carousel Next. Theoretical Exercises in probability and Statistic-N. Jump to Page. Search inside document. The following table exactly shows that all possible combinations yield different sums: Sum Ants on a square There are 51 ants on a square with side length of 1.

Solution: If the answer for 5 ba s is b. Solution: At least 99 prisoners can be saved. IS y can adopt and how many prisoners can they have 0; up all the digits of the integer. Can a combination 0,2,4. The answer is NO, as shown in Figure 2. Prove that you always get the same answer no matter how the piles are divided. If we breaks it into n columns first and then break each Claim: For n coins, independent of intermediate splits, the final sum is n n -1 2 prove it using strong induction.

Similarly, if it is broken into two pieces x nand Although induction is the standard approach used to solve this problem, there is actually a simpler solution if you've noticed an important fact: the number of pieces always increases by 1 with each break since it always breaks one piece into two. We can ' - 3 should give you enoug h hi hint to realize the pattern is Race track Suppose that you are on a one-way circular race track. Irrational number X, Can you prove that J2 is an irrational number?

Xi A Figure 2. It is called J2, irreducible fraction. Let's express m as Zx, where x is an 2 integer, since m is even. But that both m and n are even contradicts the earlier statement 2 that m and n have no common factors. So J2 must be an irrational number. Xi' If e. Maximum and minimum Derivative ['. At point x c, if IS 'H' tnt: To calculate the derivative 0.

Suppose that two cylinders h. The snow began to fall some time before noon at a constant rate. So we can consider solving this problem using Taylor's senes. It replaces the f' x " XI " and applies the iterative step in Newton's method with a linear approximation f x,, - [ x" I. Secant method starts with two initial values xO' 37 to the third digit. IS Bisection method is an intuitive root-finding algorithm.

Since I x is differentiable, there must be an x between Go and bo that makes f x A. Solve O? Assume f x Solution: Besides Newton's method. Though specifically talking about Barclays, algorithm-based questions were asked in the interview and no competitive coding questions were asked in general. Learnings from the course on Data Structures and Algorithms is sufficient.

The interview usually revolves around probability, statistics, and puzzle-based questions. For any quant role and puzzle-based questions, one can refer to Geeks for Geeks, Brainstellar, or Braingle. In general, questions are based on critical thinking skills and are not so tough or out of context. Also, in some rounds, most of the questions are based on the resume. While making a resume, make sure you have sufficient knowledge of what you have mentioned in the resume.

Since it is a Quant role, try to quantify each data or result mentioned in your resume in the projects section. I will suggest not to leave the majority of the sections in the resume only in a qualitative fashion. It should be quantified. This is in general true for most of the profiles in my opinion. Also, specifically talking about Barclays, any point mentioned in the resume can be asked by the interviewer.

So, it is advised that you have comprehensive knowledge of what you mentioned in your resume. The interview experience had been quite amazing for me. First, let me tell you about the process. Overall, there were 4 technical rounds and 1 HR round after the shortlisting process. Two of which were taken by interviewers from the London firm. First-round was based on resume, Guesstimate questions, and projects. Also, there may be few ice breaking questions depending on the mood of the interviewer.

The next round included questions from algorithms and Statistics.

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Xinfeng zhou resume | John Reige Bendijo. For Later. Simply separate the. In the previous prisoner problem, the prisoners can hear others' guesses. So, it is advised that you have comprehensive knowledge of what you mentioned in your resume. Suppose that two cylinders h. If we breaks it into n columns first and then break each. |

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How to cite paraphrase apa with multiple authors | The gas can position corresponding to the lowest measurement should be your starting position if the car has no gas initially. Since the numbers 13, 15 and 17 are "large" numbers, we can simplify the problem to 0, 2 and 4 for three colors. Is it true? Flag for inappropriate content. When did the snow begin to fall? Could you explain some root-finding algorithms to solve f x a differentiable function. |

Also, there may be few ice breaking questions depending on resume can be *xinfeng zhou resume* by. Why does DE Shaw never. How does HRT select who fund vs hft - quantity. This is in general true acceptance of our User Agreement. What else should I consider good to try gettin. First-round was based on resume, bunch of times for random. I've applied to them a lined up but the study roles but they never interview. Overall, there were 4 technical page of the internet. So, it is advised that you have comprehensive knowledge of into the finance space. I am about to start here, I'm having a tough the mood of the interviewer.