13-20. If V(X) = V(Y) = 7 and V (X - Y) = the correlation coefficient between random%3Dvariable X and Y is(i) -:(ii)} ;

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Answered: 13-20. If V(X) = V(Y) = and V(X - Y) =…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Imagine that there is a correlation of r = 0.65 between variable X and variable Y. Based on the correlation between these two variables (and only these two variables), what is a person's predicted value on variable Y, when his X value on variable X is a z score of 1.5? Please provide your answer as a z score with a minimum of three decimal places.
11. Define the correlation coefficient ry between the variables x, y. ху Show that r will be positive or negative according as Oxy > or < 6x – y- Given x= 4y + 5, y = kx + 4 are the regression lines of x on y and y on x respectively, show that 0sks. If k= find the means of the two If k = 4' variables and the coefficient of correlation between them.
What is indicated by a Pearson correlation of r= +1.00 between X and Y? O Every increase in X causes an increase in Y Every change in X causes a change in Y O Each time X increases, there is a perfectly predictable increase in Y All of the other 3 choices occur with a correlation of +1.00.
10 10 10 10 10 (I) If Ex, = 65, Ey, = 40, >x =925, Ey = 400 and Ex, y, = 584, then find i=1 i=l i=1 i=1 i=1 the correlation coefficient between X and Y.
Question 2. Show that, for a simple linear regression, R² = ry, where R² is the coefficient of determination and rxy is the sample correlation between Y and X. Hint: Σ" (Υ - Y)2 Σ1(Y₁-Y)²¹ SxY √SXXSYY' where Sxy = 1 (X; — X)(Y; — Y), Sxx = ₁1(X; - X)², Syy = ₁₁(Y₁ - Y)². R² = "XY =
For two variables X and Y, we have two regression lines 2X-7Y+3=0 and aX+bY+6=0 for some constants a and b. Suppose we know that X = 2 and Y = 1. Also the second regression line passes through (4, 5). Find the correlation coefficient of these two lines.
Find the equation of the least-squares regression line ŷ and the linear correlation coefficient r for the given data. Round the constants, a, b, and r, to the nearest hundredth. {(1, 4), (3, 6), (5, 11), (7, 15), (11, 23)}
Allustration 27. For a bivariate data, you are given the following information: E(X- 58) = 46 'EXX - 58)? = 3086 E(Y- 58) = 9 E(Y- 58)* = 483 E(X – 58) (Y– 58) = 1095 Number of pairs of observations = 7. You are required to determine (i) the two regression equations and (ii) the co-efficient of correlation between X and Y series. %3D %3!
Example 3 : The tangent of the angle between two regression lines is 0.6 and if 1 =-0,, find the correlation coefficient between x and y. 2

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13-20. If V(X) = V(Y) = and V(X - Y) = the correlation coefficient between random %3D variable X and Y is (i) -: (iin :