Let N be the last digit of your student number. Let X and Y be two continuous random variables that havethe correlation coefficient c=0.1(N+1). Which of the following statements are true? (Wrongly tickedanswers will reduce your marks in this question)a. X and Y are positively correlated.b.O c.X and Y are statistically independent.The sum of E[X] and E[Y] is equal to E[X+Y].Od. X and Y are negatively correlated.e.The sum of Var(X) and Var(Y) is equal to Var (X+Y).

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Answered: Let N be the last digit of your student…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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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J 2 Uncorrelated random variables are not necessarily independent, however. A special situation occurs in the case of jointly Gaussian random variables. For the Gaussian case, uncorrelated random variables are also independent. I donot understand thses sentence. Please explain it through an example.
Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of “girls” (g) and “boys” (b), which we write gbg, bbb, etc. For each outcome, let R be the random variable counting the number of girls in each outcome. For example, if the outcome is bbb, then R(bbb)=0. Suppose that the random variable X is defined in terms of R as follows: X=R^2-2R-1. The values of X are given in the table below.
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Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of "girls" (g) and "boys" (b), which we write gbg, bbb, etc. For each outcome, let R be the random variable counting the number of girls in each outcome. For example, if the outcome is bbg, then R(bbg) = 1. Suppose that the random variable X is defined in terms of R as follows: X=R- - 2R-4. The values of X are given in the table below. Outcome bbb ggb bbg gbg gbb bgg bgb gg Value of X-4 -4 -5 -4 -5 -4 -5 -1 Calculate the values of the probability distribution function of X, i.e. the function py. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X Px (x) E 1:48 PM 3/21/2022 hp Compag LAI956X 立

Compute the value of the multiple correlation (R). You should use a computer to find the solution. Y X1 X2 X3 27.6 1 4 4 9.4 3 5 3 15.6 4 7 1 20.3 5 5 4 12.3 3 7 3 8.7 5 3 6 7.3 7 5 7 14.9 6 4 8 17.0 5 3 9 -0.8 4 2 0
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Let N be the last digit of your student number. Let X and Y be two continuous random variables that have the correlation coefficient c=0.1(N+1). Which of the following statements are true? (Wrongly ticked answers will reduce your marks in this question)