Theorem 3.1 (The Cauchy-Schwarz inequality) Suppose that X and Y have finite variances. Then |EXY
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- Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; isLet X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Let X and Y have joint PDFfX,Y (x, y) = 3x^2y + 3xy^2 if 0 < x < 1, and 0 < y < 1 0 otherwise.a) Find the covariance of X and Y .b) Find Var(X).c) Find the correlation of X and Y (X and Y have the same variance.)
- Let X1, X2, X3 be independent Exp()-distributed random vairables. Determine the pdf of X(1)X(3)Type II error occurs when an individual fails to reject H0 when H0is false. True or False?(a) Use the rules of expected value to show that Cov(ax + b, cY + d) = ac Cov(X, Y). Cov(ax + b, CY + d) = E - E(ax + b)E ])-) + adx + bcY + bd - (aE(X) + b) CE = = acE + adE(X) + bcE(Y) + bd + adE(X) + bcE = acE acE(X)E 1)) = — асCov(X, Y) (b) Use part (a) along with the rules of variance and standard deviation to show that Corr(ax + b, cY + d) = Corr(X, Y) when a and c have the same sign. co( b, cY + Corr(ax + b, cY + d) = Oax + bº cY + d Cov(X, Y) la||clox0y Corr(X, Y) lallc| = Corr(X, Y) (c) What happens if a and c have opposite signs? ac O When a and c differ in sign, ac is negative and = -1. Therefore, Corr(ax + b, CY + d) = -Corr(X, Y). la||c| ac O When a and c differ in sign, ac is positive and = 1. Therefore, Corr(ax + b, cY + d) = -Corr(X, Y). Jal|c ас O when a and c differ in sign, ac is positive and = 1. Therefore, Corr(ax + b, cY + d) = Corr(X, Y). lal|c ac O when a and c differ in sign, ac is positive and = -1. Therefore, Corr(ax + b, cY + d) = -Corr(X, Y). la||c| ас O…
- Let X1, X2,..., X, is a random sample from a distribution with density function f(x; 0) = 302e-0³ for 0Prove that cov(X, Y) = cov(Y, X) for both discreteand continuous random variables X and Y.please answer it during 1 hoursLet X be a random variable with pdf: f(x)= k(10 - 2x) for x being [0,5] a.) Find k b.) Find E(X) c.) Find Var(X) d.) Find E(3 *squareroot(X))Q4) The probability mass function of Y is f(y) = y/6 for y=1,2,3,4. Find the variance of Y.6. Suppose the moment generating function of X is M(t) = ² et + e²t+e³t. a) Find the mean of X. b) Find the variance of X. c) Find the pmf of X.SEE MORE QUESTIONS
