0, y > 0cxfx,Y0.W.where c is some constant.Question part 1: _(Answer by selecting the correct choices from the dropdown menusbelow)We need to figure out the value of c. In order to do this, we...

Extracted text: Let X, Y have the joint pdf for x? + y? < 1="" and="" a=""> 0, y > 0 cx fx,Y 0.W. where c is some constant. Question part 1: _(Answer by selecting the correct choices from the dropdown menus below) We need to figure out the value of c. In order to do this, we need to evaluate the definite double integral below, but first we need to figure out the limits of integration denoted by x1ow , Xhigh , Ylow » Yhigh Xhigh Suhish Soh ca dædy Ylow xlow Note that in the double integration above, we will do dx and then dy. I strongly recommend that you use a piece of paper to sketch the support on the x, y plane. Xlow [ Select ] Xhigh [ Select ] %3D [ Select ] Ylow = [ Select ] Yhigh %3D Xlow [ Select ] [ Select ] X high sqrt( 1-y^2) Ylow - sqrt( 1 - y^2) sqrt( 1 - x^2) Yhigh [ Select ] Xlow [ Select ] X high %D [ Select ] Ylow sqrt( 1 - x^2 ) sqrt( 1-y^2 ) Yhigh = %3D 1-y^2 1 Note that in the double integration above, we will do dx recomr [Select ] per to sketch the s sqrt( 1 - x^2) Xlow Chigh - sqrt( 1 - x^2) Ylow [ Select ] %3D Yhigh %D ISoloct 1 Xlow [ Select ] 1 Xhigh = sqrt( 1 - y^2) sqrt( 1 - x^2) Ylow = %3D Yhigh = %3D <> > >


Extracted text: Question part 2: What is the value of c that makes this a proper joint distribution (i.e. integrates to 1 over the support)? O 3/2 O 1/3 O 3 O We do not have enough information to answer this question. Question part 3: find fx (x), the marginal distribution of X. (Answer choices are given in terms of c) O fx(x) = cx/1 – x² for 0 < x="">< 1,="" and="" o="" otherwise="" o="" fx(x)=";(1" –="" y?)="" for="" 0="">< x="">< 1-="" y²,="" and="" o="" otherwise="" o="" fx(x)="c(1" –="" y²)="" for="" 0="">< x="">< 1,="" and="" o="" otherwise="" o="" fx(x)="cx" 1="" –="" x²="" for="" 0="">< v/1 – y², and o otherwise v/1="" –="" y²,="" and="" o="">