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Mean and Variance The main point of this lecture is to tie those concepts back into sigma notation, which is one of the main uses for summation. We’ll walk through this very slowly and unpack it for you. If we have a set of numbers X, with N numbers in them (XI to Xh) they’re…

Vector examples in 2 dimensions We draw a vector as an arrow. In this example, v is a vector, and we can describe it with two numbers: v1 and v2. [Graph] The vector v will be written as [vi, v2]. v->=(v_1,v_2) Some people write vectors in one way, and others write them another way. You…

How Logarithms and Exponents are Related Logarithms and Exponents are inverse functions of each other. Logarithms are the exponent that is necessary to raise a number to produce a given number: Exponents are the logarithm of a number whose base is 1. The product rule is used to calculate the derivative of the product of…

Critical points definition In this section, we will learn how to use partial derivatives to solve optimization problems. For today, we will examine the function of two variables. However, this concept can be applied to any number of variables. In 10 years, when you have a real job, your job might be to minimize the…

Session 18-Reading 69, The Theory of Active Portfolio Management-LOS c (Practice Questions, Sample Questions) Session 18: Portfolio Management: Capital Market Theory and the Portfolio Management ProcessReading 69: The Theory of Active Portfolio ManagementLOS c: Describe how an analyst’s accuracy in forecasting alphas can be measured and how estimates of forecasting can be incorporated into the Treynor-Black…

Volume and Surface Area of Prisms and Pyramids A pyramid is a polyhedron whose base is a polygon and whose faces are triangles that meet a common vertex. Lateral faces are the faces of a prism or pyramid that are not bases. The surface area of a prism or pyramid is the sum of the…

Introduction to Mathematical Thinking. Tutorial for Assignment In problem 7, we must negate statements and put them in positive form.Part A asks us to prove that for all integers “x” in N, there exists an integer “y” in N such that X plus Y equals 1. The negation of this statement is: If an integer…

CFA Level 1 – Portfolio Management, Session 18 – Reading 61 (Notes, Practice Questions, Sample Questions) 1. Which of the following are least likely key assumptions of the CAPM? A)Investors can borrow and lend at the risk-free rate.B)Investors throughout the world have identical consumption baskets.C)Unlimited short selling is allowed with full access to short-sale proceeds Explanation…

The Cartesian Plane In the 17th century French mathematician, René Descartes, while in bed because of an illness, was watching a spider on the ceiling. As he watched, he thought of how he might describe the position of the spider at any instant. The technique he designed is called the Cartesian Coordinate System.All proper graphs…

CFA Level 2 – Financial Reporting and Analysis, Session 7 – Reading 26 (Practice Questions, Sample Questions) 1. Consider the following statements:Statement 1:Compared to the cash basis of accounting, the accrual basis of accounting provides more timely information about future cash flows.Statement 2:Compared to the cash basis of accounting, the accrual basis requires more use…