Question

5. In studying the behaviour of air support roofs, the random variables X, the inside barometric pressure (in inches of mercury), and Y, the outside pressure, are considered. Assume that the joint density for (X Y) is given by с /х 27 < у <x< 33 fxxx, y) = otherwise A. Find c B. Find fx(x) and fyy) C. Find P(X30 and Y<28).

Answer 1

Given fy (GY) = 5 4 3 292 y 2 2533 lo; otherwise A). We know that $(fea,y) dady=1 Še dedy = 1 7=27,4=27 = 1 3=274 27 La tylko Sasa [** - $(27)}da=1 (-25)dx=1 c[_24bg] = [23–24log 3a)–(24–2769270] = c(-7,9999 + 11.6468] =1 2=27 27 3.6469C= C= 3.6469 C= 0.2742

| B.A) = CRCnDay 242 한 - 0.2442 [] = 0.242. [24] SC) = 0.2742 - 다. 4034

fy(y) = {fq,y) de F S 0.2742 1dx = 0.2442 [loga) = 0.2742[log33-log28] fyly)= 0.0239 C) P(X330,4528) = 530 58 8.2442 £ dady 1942. Canada - 130 0.2742 (18–24) de = 0.2742 (logazgo = 0.2442 (log30–1927) 2=27y=27 9=27 a 27) da = 0.0125