A candy company distributes boxes of chocolates with a mixture of creams, toffees, and cordials. Suppose that the weight of each box is kilogram, but the individual weights of the creams,toffees, and cordials vary from box to box. For a randomly selected box, let X and Y represent the weights of the creams and the toffees, respectively, and suppose that the joint density function ofthese variables is as shown. Find the covariance between the weight of the creams and the weight of the toffees in these boxes of chocolates.1384xy, 0≤x≤f(x,y) =0,elsewherex+ys.

Detailed explanation: To find the covariance between the weight of the creams XXX and the weight of…

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

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A candy company distributes boxes of chocolates with a mixture of creams, toffees, and cordials. Suppose that the weight of each box is 1 kilogram but the individual weights of the creams, toffees, and cordials vary from the box to box. For a randomly selected box, Let X and Y represent the weight of the crems and the toffees, respectively, and suppose that the joint density function of these variables is | 24xy 0
3. A candy company distributes boxes of chocolates with a mixture of creams, toffees, and cordials. Suppose that the weight of each box is 1 kilogram but the individual weights of the creams, toffees, and cordials vary from the box to box. For a randomly selected box, Let X and Y represent the weight of the crems and the toffees, respectively, and suppose that the joint density function of these variables is 24xy 0
A student has 3 volumes of short stories and 2 novels on a bookshelf. She selects 3 books at random to take home over vacation. A random variable X is defined to be the number of novels selected. Find the values assumed by X and its density function.
Astronomers use a technique called stellar stereography to determine the density of stars in a star cluster from the observed (two-dimensional) density that can be analyzed from a photograph. Suppose that in a spherical cluster of radius R the density of stars depends only on the distance r from the center of the cluster. If the perceived star density is given by y(s), where s is the observed planar distance from the center of the cluster, and x(r) is the actual density, it can be shown that y(s) = J. Tr - s 2r -x(r) dr If the actual density of stars in a cluster is x(r) = }(R – r)", find the perceived density y(s).
Consider two types of investment: bonds and shares. Denote next year’s value of one unit of investment in bonds as X and one unit of investment in shares as Y. Suppose that the two types of investment are independent. The marginal density functions for X and Y are, respectively, given in table 1 and table 2: Table 1 x 24 25 26 P(X = x) 0.2 0.3 0.5 Table 2 y 48 49 50 51 P(Y=y) 0.1 0.2 0.4 0.3 a) Determine the joint probability density function of X and Y. b) Suppose that you consider building a portfolio that mixes both bonds and shares. Also suppose that the portfolio’s return can be described by the following function: U =50X −30Y −15.What are the expected return and the variance of the portfolio?
Given fty)=ky, 2sy <8, and fly)=0 clsewhere. a. Find the value of k for which fy) is a valid density function? b. Find P(1
The life (in days) of a certain machine has an exponential distribution with a mean of 1 day. The machine comes supplied with one spare. Find the density function (t measure in days) of the combined life of the machine and its spare if the life of the spare has the same distribution as the first machine,but is independent of the first machine.
Find the maximum, minimum, and tensile points of the following functions.
A shape of a university campus is a square with side length of 10 miles. If you imagine the university on the x-y plane, in the first quadrant with two sides of the square on the positive axes, then the student union is at the origin (at a corner of the square). At noon on a certain day an announcement was made that all students had to walk to the student union. At that time the density function of the students spread over campus was given by: f(x, y) = (3/20000)*(x^2 + y^2 ) 0 < x < 10, 0 < y < 10, 0 otherwise. If students are only allowed to walk parallel to the axes what is the expected value of the distance walked to the student union by a randomly chosen student on campus? (Assume that students walk in a way that monotonically decreases their distance to the student union. That is, they don’t walk ” backward”.)
variable has the density curve whose equation is ? = 2x for 0 < ? < 1, and ? = 0 otherwise. d) What percentage of all possible observations of the variable are at most 3/8? e) What percentage of all possible observations of the variable are at least 1/4? f) What percentage of all possible observations of the variable lie between 1/2 and 3/4?
A variable has the density curve whose equation is y = 2x for 0< x 1, and y = 0 otherwise. a. Graph the density curve of this variable. b. Show that the area under this density curve to the left of any number x between 0 and 1 equals x2. What percentage of all possible observations of the variable c. lie between 1/2 and 3/4? d. are at least 1/4?
If X and Y are independent RVs with pdf's e*, x20, and e, y 2 0, respectively, find the density functions of U = X and V=X+Y. Are U and V independent? %3D X + Y

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