Consider n = 5 pairs (x! ,y, , . . . , (xt, y,'). Let x = n-ı Σ i , and y = n-ı Σ -1 y be the sample means of the x and y variables. Let & and Sy be the corresponding standard deviations. Let sry and rry be the sample covariance and sample correlation respective . Suppose x = 6.2,J = 8 8 2.95, sy4.494, sy 13.05. Part a) What is the sample correlation of the...
Let X ~Par (2) and Y = ln(X). Compute P(Y > 1).
1. Let (X,Y) be a random vector with joint pdf fx,y(x,y) = 11–1/2,1/2)2 (x,y). Compute fx(x) and fy(y). Are X, Y independent? 2. Let B {(x,y) : x2 + y2 < 1} denote the unit disk centered at the origin in R2. Let (X',Y') be a random vector with joint pdf fx',y(x', y') = 1-'13(x',y'). Compute fx(x') and fy(y'). Are X', Y' independent?
(1 point) Let st, y est, z t2 2yz 3z, W = x¥ Compute дw (2,-2) (e^4+12)-2)+(4-2e^4)(-2e^4 as дw (2, 2) Әе
2.9.8 Let X~ Geometric(1/4), and let Y have probability function 1/6 y-2 y=5 0 otherwise Let W = X + Y. Suppose X and Y are independent. Compute pw (w) for all to e Ri
(1 point) -2 -5 Let x = and y= -2 Find the vector v = 3x-6y and its additive inverse.
Let X ~ N(0,1), and let Y = 2X + 5. Compute P(Y <= 7)?
2. Let и(x, y, 2) ='y+y23, t = rse", y = rse- = r’s sint Compute ди ди at the point r = 2, 8= 1, t= 0 дѕ' де ət ди
(1 point) -1 -3 -2 Let y = 3 , U1 = -2 -5 2 U2 = -7 -1 16 Compute the distance d from y to the plane in R’ spanned by uj and u2. d=
A is the point (-1, 5). Let (x, y) be any point on the line y = 3x. a Write an equation in terms of x for the distance between (x, y) and A(-1,5). b Find the coordinates of the two points, B and C, on the line y = 3x which are a distance of √74 from (-1,5). c Find the equation of the line l1 that is perpendicular to y = 3x and goes through the point (-1,5). d Find the coordinates...