Question 6 The Wall Street Journal reported that almost all the major stock market indexes had posted strong gains in the last 12 months ("What's Hot...and Not," The Wall Street Journal, April 26, 2014, C3). The one year return for the S&P 500, a group of 500 very large companies, was approximately +27%. The one year return in the Russell 2000, a group of 2000 small companies, was approximately +52%. Historically, the one-year returns are approximately normal. The standard deviation in the S&P500 returns is approximately 20%, and in the Russell 2000 the standard deviation is approximately 35%. a. What is the probability that a stock in the S&P500 gained 30% or more in the last year? Gained 60% or more in the last year? b. What is the probability that a stock in the S&P500 lost money in the last year? Lost 30% or more? Repeat (a) and (b) for a stock in the Russell 2000.
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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