Consider two random variables X and Y possessing the following joint pdf:2x + y0>t.

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Answered: Consider two random variables X and Y…

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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There are two independent random variables X and Y. X has mean 4 and standard deviation , and Y also has mean 4 and standard deviation . A random variable Z is the sum of X and Y. That is, Z = X + Y. Calculate the mean of Z.
Practice Question 2: Let X₁ a random variable with expected value (mean) E(X₁) = 17 and variance V(X₁) = 12. Let X₂ another random variable with expected value (mean) E(X₂) = 22 and variance V(X₂) = 16. The covariance between X₁ and X₂ is Cov(X1,X 2)=9. Let a new random variable Y defined as Y = 9X₁ + 10x₂. a. d. Explain briefly the meaning of the correlation of these two random variables X₁ and X2. e. Explain briefly if X₁ and X₂ are linearly independent not.
Let X be a discrete random variable that takes values -1, 0, and 1 with probabilities 0.2, 0.5, and 0.3, respectively. What is the variance of X?
O Three uncorrelated random variables X1, X, andX3 have means 1, - 3 and 1.5 and second moments 2.5, 11 and 3.5 respectively. Let Y = X1- 2X2+ 3X3 be a new random variable. Find (a) mean value (b) variance of Y.
TABLE 13-6 -1 0. 13-21. Let X and Y be two random variables each Y taking three values -1, 0 and 1, and having the joint probability -1 1. distribution as given in Table 13-6. 2 Obtain the marginal probability distributions of X and Y and hence their expected values.
O Prove that E(X) = E(X/Y), where X and Y are two random variables which are independent. %D
If X and Y are independent, normally distributed random variables each with mean 0 and variance 1, then 2X + 2Y: Select one: a. has a normal distribution with mean 2 and variance 10 b. has a normal distribution with mean 2 and variance 8 c. has a normal distribution with mean 0 and variance 10 d. has a normal distribution with mean 0 and variance 8 e. has a normal distribution with mean 0 and variance 5
Let X and Y be independent random variables with μX = 3, σX = 3, μY = 2, and σY = 3. Find the mean and variance of X – Y. The mean of X - Y is . The variance of X - Y is .
Let X,, X2, and X3 be independent random variables, each are binomially distributed with n = 100 and p = 0.2. Let A = X,– 2X2 and B = X3 + 3X1. Find PAB- %3D %3D
The table gives the joint probability distribution of the number of sports an individual plays (X) and the number of times she may get injured while playing (Y) X=1 X=2 X=3 0.12 0.08 0.15 0.06 0.05 0.05 0.10 0.03 0.15 0.15 0.04 0.02 Y=4 Y=3 Y=2 Y=1 The covariance between X and Y, oxy, is (Round your answer to two decimal places Enter a minus sign if your answer is negative) The correlation between X and Y, corr(X, Y), is (Round your answer to two decimal places Enter a minus sign if your answer is negative.) An increase in the number of sports an individual plays will tend to * the number of times she may got injured while playing

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Consider two random variables X and Y possessing the following joint pdf: |2x+ y 0