A5 A-If you use only the x-axis what is the variance loss B- if you use a diagonal line what will be the loss on variance
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Q: loss b. if you use a diagonal line what will be the loss on variance
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A-If you use only the x-axis what is the variance loss
B- if you use a diagonal line what will be the loss on variance
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- Let X and Y be random variables, and a and b be constants. ???? a) Show that Cov [aX,bY] = abCov [X,Y] . b) Show that if a > 0 and b > 0, then the correlation coefficient between aX and bY is the same as the correlation coefficient between X and Y . c) Is the correlation coefficient between X and Y unaffected by changes in the units of X and Y ?13) Random variables X and Y have joint pdf fXY={4xy, 0≤x≤1, 0≤y≤1fXY={4xy, 0≤x≤1, 0≤y≤1 Find Correlation and CovarianceHow to solve this using Microsoft Excel Use alpha of 0.05 2 tail. Free Association (in seconds) Partially Controlled (in seconds)5.84 4.844.64 5.643.56 8.565.00 7.002.35 4.353.67 4.677.87 6.677.74 5.444.48 5.586.56 6.26
- Let X and Y be random variables, and a and b be constants. a) Prove that Cov(aX, bY) = ab Cov(X,Y). b) Prove that if a > 0 and b > 0, then ρaX,bY = ρX,Y. Conclude that the correlation coefficient is unaffected by changes in units.The joint probability mass function p(x,y) of X and Y is defined as follows: p(0,0)=0.5 p(1,0)=0.2 p(0,1)=0.2 p(1,1)=0.1 a) What is the covariance between X and Y? b) What is the correlation coefficient of X and Y? c) Are X and Y are dependent? What about are X and Y are uncorrelated?1. Find the population covariance between X and Y .2. Find E[Y |X = x].3. Find Var[Y |X = x].
- 1)A random vector z = (x y) T has a joint probability density given by:a)Determine the correlation matrix of the z vector.b)Determine the covariance matrix of vector z.c)Determine if the v.a.s x and y are independent.X is the Gaussian (μ=1, σ=2) random variable. Y is the Gaussian (μ=2, σ=4) radnom variable. X and Y are independent. a) What is the PDF of V = X + Y b) What is the PDF of W = 3X + 2YA stochastic process (SP) X(t) is given byX(t) = Asin(ωt + Φ)where A and Φ are independent random variables and Φ is uniformly distributed between 0 and 2π.a) Calculate mean E[X(t)]. b) Calculate the auto-correlation RX (t1,t2).c) Is X(t) wide sense stationary (WSS)? Justify your answer.Now consider that X(t) is a Gaussian SP with mean μX (t) = 0.5 and auto-correlation RX (t1,t2) =10e−14 |t1−t2|. Let Z = X(5) and W = X(9) be the two random variables.d) Calculate var(Z), var(W), and var(Z + W). e) Calculate cov(ZW).
- Consider the information below relating to the monthly rates of return for two companies X and Y over a period of 4 months: Y 2 xRate of return yRate of Return Date Month 1 -4.76 -4.75 Month 2 5.34 7.65 Month 3 12.09 6.98 Month 4 -2.98 9.65 Calculate the covariance per month between the two companies. Show all your working.Let X1,X2,X3 be random variables such that E(Xi) = μ and Var(Xi) = σ2 for all i. Find the value of the following quantities (as a function of μ and σ2) if the Xis are all mutually independent. Then repeat these calculations if each pair of variables have a correlation of ρ, that is, corr(Xi, Xj ) =ρ for i ≠ j. (a) E(X1 −X2 +X3) (b) Var(X1 − X2 + X3) (c) E(X21 − X22 + X23)Fill-in the table by computing X2, Y2, XY, and the total (sum) After filling in the table completely, compute the Pearson Product-Moment Correlation Coefficient (refer to pgs. 80-81) X Y X2 Y2 XY 3 2 4 4 7 5 6 6 3 6 8 3 9 8 8 7 2 2 5 5 Total, Sum ∑