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et X, Y have the joint pdf | cx for æ2 + y? < 1 and x > 0, y > 0 fx,Y O.w. here c is some constant. uestion part 1: (Answer by selecting the correct choices from the dropdown menus elow) le need to figure out the value of c. In order to do this, we need to evaluate the efinite double integral below, but first we need to figure out the limits of integration enoted by xlow, X'high, Ylow , Yhigh CUhigh Lhigh cx dxdy Ylow Jxlow ote that in the double integration above, we will do dx and then dy. I strongly ecommend that you use a piece of paper to sketch the support on the x, y plane. [ Select ] low = [ Select ] %3D high [ Select ] Cow =

et X, Y have the joint pdf | cx for æ2 + y? < 1 and x > 0, y > 0 fx,Y O.w. here c is some constant. uestion part 1: (Answer by selecting the correct choices from the dropdown menus elow) le need to figure out the value of c. In order to do this, we need to evaluate the efinite double integral below, but first we need to figure out the limits of integration enoted by xlow, X'high, Ylow , Yhigh CUhigh Lhigh cx dxdy Ylow Jxlow ote that in the double integration above, we will do dx and then dy. I strongly ecommend that you use a piece of paper to sketch the support on the x, y plane. [ Select ] low = [ Select ] %3D high [ Select ] Cow =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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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 <> > >
Transcribed Image 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 <> > >
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 <x < V/1 – y², and O otherwise
Transcribed Image 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 <x < V/1 – y², and O otherwise
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