Question

(1 point) Let f(x Scxºy? if 0 < x < 1, 0 SY51 otherwise Find the following: (a) c such that f(x,y) is a probability density function: c= (b) Expected values of X and Y: E(X) = E(Y) = 100 (c) Are X and Y independent? (enter YES or NO)

Answer 1

fied = cх² y² ORALI, Deyal We know that, I E (g): So soy ferry dardy 1 - Solo y gon' ytandy =/o8or sayede dy So'yldy sosox de =8043] (6) = 80UJ )0) cx*%=1 ELA)) = So Soxy Ferry) andy Eso lo sono go dx dy • [/0-%0] =1 c=80 • ELHI = ' S x Flxif) dx dy = 80[%] [%] = 80/99 © xey are independent if Elxiy) = E(X) Ery) R.4.5 = E(X)E) • S.V: *80 x?y? te dy • = 307" loytay dx LH.5 = Eiwy) - 99 - From ② 46 EIGY) = Ex) Ely TH) x 4y are independent

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