Q23. Consider random variables Y, and Y. related to arbitrary random variables x and Y by the coornate rotation. Y, = X cos 0 + Y sin 0, Y, = -X sin 0 + Y cos 02%3D%3D6.(i)Find the covariance of Y,, Y, and CyY,

Answered: Q23. Consider random variables Y, and…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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2. Given the Cartesian coordinates x = 300 mm with standard deviation o, = 0.04 mm, and y = 400 mm with standard deviation ay - 0.05 mm. Assume x and y are uncorrelated. Compute the polar coordinates r and 0 and their variance-covariance matrix
a and b please and thank you
Determine the following (by providing the numeric answer). a. ZY= 2) b. Σy2 – (ΣΥΖ c. ({})² = d. (EX)(EY) e. ΣXY – f. Σ(X-Y) = Using the following data set: XI – 3 NG* 9 --ANK 10 S S
P/oblem 8. Given x, = Px, + w,, where w, is white but not gaussian. What is the mean and covariance equation for x, ?
Jhe The cross psd is given as 1 Sxy (@) a>0, a is a constant ΧY (a+ j@) Find the cross correlation function and average power.
S:55)
Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: y USE SALT 2= Σχ = 15; Σy = 88.3; Σx2 = 55; Σy2 = 1,594.89; Σxy = 275.8 (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.) X= y = b= ŷ= (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. y y 22 20 18 16 14 12 10 0 y 22 20 14.4 18 y 22 VX 20 18 16 14 12 10 5 1 (c) Find the sample correlation coefficient r and the coefficient of determination 2. (Round your answers to three decimal places.) 16 14 12 5 2 3 4 19.9 14.4 19.6 20.0 1 1 2 2 3 3 4 4 5 22 6 20 18…
S
4. The arcsin distribution has the CDE and inverse CDF below. Using, .25, .74, and 46 as random numbers, generate the corresponding iterates from the arcsin distribution in radians. (Provide your answer in the form YO, Y1, Y2 and round answers to two decimal places.) p-¹(u) = (sin(u) ². F(x) = 2 πT arcsin (√),
Suppose that X and Y are random variables with E(X) = 1, E(X²) = 5, E(Y) = 3, and E(XY) = 1. Match up the following quantities. Cov(X,Y) Corr(X, Y) Var(-X/2) Cov(X/2,-2Y + 3) Drag answer here Cannot be determined Drag answer here Drag answer here 2 Cannot be determined 1
#2 and #3 of Example 2.6
Which one of the following is the covariance of the given variables X and Y? x=X-X y%3DY-Y X-X)( Y-Y )=xy Y 3 12 20 1 7 10 23 5 18 24 11 30 2 10 48 144 Select one: 156.25 25.88 12.5 53.75

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Q23. Consider random variables Y, and Y. related to arbitrary random variables X and Y by the coo nate rotation. Y, = X cos 0 + Y sin 0, Y, =-X sin 0 + Y cos e (i) Find the covariance of Y,, Y, and Cy,Y, 13