Question

that E{E(Y|X) = E) (3 marks) If the random variable X has p.d.f. - SXSTE f(x) = {20 'o, otherwise, y = ex Gly)= Prob (Ys y) = Probe Prob(ancex) sluca inly) x < lncy F(x) dx = e cumulative distribution function technique to determine the p.d.f. of Y=e (4 marks CJE marks) avoy Given that the continuous random variable X and Y have joint p.d. f. f(x,y). She

Answer 1

WTH #Given that the continuous random variable x and y have voint pdf 16,4) shon E{ECY\x)} = ECT) E Orlx) = Sy fulx (atx) dy is the conditional expectation of r1x= x = m (x) say. €(x) = SS y f(x,y) dxdy. Range Range SS y frix (sla) sla) dady [sla) is the marginal pockf А of x] S[ Sy frix (312) dy] g (as da [A is the set of all x with positive density Sma) a Cal de こ А = € (mm(x)) = E (E6r1x)) m@)-681x) - Hence the proof. fa) otherise. pdf ofx 의 . Y= ex 9 the cumulative distribution function F* (A) = P Cp Ly Plex Ly) = P(met į my = P(x < my hy = logarithen my borse' e'. & ada 1 (my +T) 27 -X 25 lay 20 2 p. d f of Y= 2 * (2) = 1 :p.df of Y , say g(y) = L RRY 2ty [-Aenea -) en Lea Let sine et 12] et Lulet othermi