Answer Happy

The joint probability density function of the random variables X, Y, and Z is given to the right. Complete parts (a) through (d). 3xyz? 64 0<x< 1, 0<y<2,0<z<4 2 f(x,y,z)= 0, elsewhere

1 <X 3 2 Y-, 3<< Z 2' 3' 3 2 133 Y 3<Z4= (e) Find P (< <x<ğiv. 2«234) 3 < [<z Plzxxaži važ,3<2<a] - 1,950 (9) Find pſo<x<*|v=1,2-4) <x1 plo<x<|v=3,2-4)- x- (Simplify your answer.) d<x YE Z= 7 Y Z = (Simplify your answer.) 49 64

(a) Find the joint marginal density function of Y and Z. Select the correct choice below and fill in the answer box to complete your choice. O A. g(x,y) = for 0<x<2 and 0<y<1 XB. g(x,z) = for 0<x<2 and 0<z<5 6 C. gly,z) = Fy?z, for 0 <y< 1 and 0 <z«5 25 (b) Find the marginal density of Y. Select the correct choice below and fill in the answer box to complete your choice. O A h(z) = for 0 <z<5 OB. h(x) = for 0<x<2 © C. h(y) = 3y2', for 0 <y<1