Question

Problem #7: Suppose that the random variables X and Y have the following joint probability density function. f(x, y) = ce-5x – 3y, 0 < y < x. (a) Find P(X < 2, Y < 1.). (b) Find the marginal probability distribution of X. Problem #7(a): Problem #7(b): Enter your answer as a symbolic function of x, as in these examples Do not include the range for x (which is x > 0).

Answer 1

Problem #7 Suppose that the random variables X and Y have the follocong Joint probability density function. f(x,y) = c.ex-3y , ocyan s f(X14) dz dy = 1 (X,Y) x . 097 0254-38 dy dk = 1 <s*zse (16**) dz=1 ( 5 ) =1 $( 55) = 1 $16) = 1 Te = 40 f(x,y) = 40.0 5x 39 ; ocu<x Q.) find PCX<2, 42+) x<2, ye h and ocyer {ocyana 1 2 3 u { 0<4 < t t ex <q} -34 24 14 wazu 0, engx-3y ó. 40.e 00% 114 401 - 14.

40[{15 - ) -(*)3 + (-e*24) (2014-EO)] 1-[(80514-52%) -8 (-8314) (79"*eto] 1-( 881514-5ē? -8 ( 8514_80_8'te 1)] -Ź ( 88914_5€4-8734 8ėtot 87%_824314] işs 3é2 +8 '0_824314] ~ 0.8646 b) Find the marginal probability distribution of X. fyca) = 5 fxy CXry) dy. ý oc fx (0) = 40 f e 5x-3y dy fyex) = 40.25% leverera fx(x) = 40. 75x Cl-232) fx C022 $ 40 (752_Bx) ; 0<x< as ; otherwise 0< x< 0 <x < og