Question

Question (c) Suppose you have two jointly distributed random variables, X and Y. Suppose you know the following facts. • Var(–7.5 X) = 53.2925 • Var(1.5 x Y) = 1.01765 • Var(2 x X +3 + Y) = 6.26319 i. What is Cov(X,Y)? ii. What is the correlation of X and Y? iii. If you had a random sample of observations of x and y and estimated the regression Y = Bo + BiX +€ What would the

Answer 1

Given that vor (-7-5 xx) = 1) 53.2925 1.0/765 = 6026319 3) vol (2xx+ 37) voe (-7.5 x) S6.25ol() = 53 • 295 = 53 0295 $3.295/1k 56.25 vozca) vor C3)= oo9474 1.o1765 voa (l.s x P = 20256VoelY)= lo01765 Vorlt) = .01765 vo)= 0.4522 %23 Let Conoidez vor (ex x + BY) = 6. 26 319. voe (2x +34)= vor(2x)+ VO (34) + cov (2x, 34 4 voe cx)tg voz c) + 6 covcx) 6.26319 4x0.9474t9 x 0.45 22 +6 covexy %3D

CovCx, Y)= 6.26319 7.8594 ৩-2.660951 eevex,+)= - Cozzelation: CovCA, Y), fexN)= Let O o9733 ০ 672.4 6%= fia4)= 0,266 035 0•9733x0.6724 ean ot Reqzession is Y= BotP,x fE find. wOomit

ECBI)= B, Oe6724 Oo4064 ০.৭+33 0.28075 ECBi) = 28075