Determine if the random variables X and Y are statistically independent or not. NO NEED SOLUTIONS 3.49 Let X denote the number of times a certain nu-merical control machine will malfunction: 1, 2, or 3times on any given day. Let Y denote the umber oftimes a technician is called on an emergency call. Theirjoint probability distribution is given as20.053.0.100.050.050.000.100.350.200.10(a) Evaluate the marginal distribution of X.(b) Evaluate the marginal distribution of Y.(c) Find P(Y = 3| X = 2).35

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Answered: Determine if the random variables X 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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Random variables X and Y have a joint PMF described by the following table. y = -1 y = 0 y = 1 3/16 1/16 0 1/6 1/6 1/6 0 1/8 1/8 x = -1 x = 0 x = 1 Are X and Y independent?
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Let X and Y be any two random variables and let a and b be any two real numbers. Then var(ax + bY) = a² var(X) + b?var(Y) + 2ab cov(X,Y). False True
Previously, you studied linear combinations of independent random variables. What happens if the variables are not independent? A lot of mathematics can be used to prove the following: Let x and y be random variables with means ?x and ?y, variances ?2x and ?2y, and population correlation coefficient ? (the Greek letter rho). Let a and b be any constants and let w = ax + by for the following formula. μw = aμx + bμyσ2w = a2σ2x + b2σ2y + 2abσxσyρ In this formula, r is the population correlation coefficient, theoretically computed using the population of all (x, y) data pairs. The expression ?x?y? is called the covariance of x and y. If x and y are independent, then ? = 0 and the formula for ?2w reduces to the appropriate formula for independent variables. In most real-world applications the population parameters are not known, so we use sample estimates with the understanding that our conclusions are also estimates.Do you have to be rich to invest in bonds and real estate? No, mutual fund…
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Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(Y)=-7 Var (X) = 20 Var (Y)=6 Var (z) = 23 E (X) = 5 E(Z) = 3 Compute the values of the expressions below. E (-2X – 4) = -3Z + 2X E 3 Var (27 + 3) - O =(-sx") - O
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uppose you reject the null hypothesis H0: μ = 101. It turns out the population mean is actually equal to 101. You have made a Group of answer choices Type I and Type II errors the correct decision Type II error Type I error
Let X and Y be two random variables such that Cov(X.Y) = -3 . Then %3D O None of these O cov(-3X+5,-3Y+5)=-18 cov(3X+5,-2Y+5)=18 O cov(5X+3,-2Y-2)=-20
Sample A Sample B s2 22 25 n 10 8 We want to test the hypothesis that population B has a smaller variance than population A.
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(Y) = 4 Var(X) = 24 Var(Y) 18 Var(z)=7 E(X)= -3 E(Z) =-1 Compute the values of the expressions below. E(-4-5X)= 0 %3D ? ()- 0 Var(-3+2.X) = 0

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