Answers
a)

b)

c)

d)


Find fxx(x,y), fxy(x,y), fyx(x,y), and fyy(x,y) for the following
function.
f(x,y)=6x/7y-9y/5x
Find fx(x,y), fxy(x,y), fyx(x,y), and fyy(x,y) for the following function. 6x 9y f(x,y) = 7y 5x fox(x,y) = fxy(x,y) = fyx(x,y)=0 fyy(x,y)=0
find fxx(x,y), fxy(x,y), fyx(x,y) and fyy(x,y) for the function f.
f(x,y)=8xe^5xy
19. Find fxx (x,y), fxy(x,y), fyx(x,y), and fyy(x,y) for the function f. f(x,y) = 8x e 5xy fx(x,y)= fxy(x,y)= fyx (x,y) = fyy(x,y) =
1.Find fxy(x,y) if f(x,y)=(x^5+y^4)^6.
2. Find Cxy(x,y) if C(x,y)=6x^2-3xy-7y^2+2x-4y-3
Find (,,(Xy) if f(x,y)= (x + y) fxy(x,y) = Find Cxy(x,y) if C(x,y) = 6x² + 3xy – 7y2 + 2x - 4y - 3. Cxy(x,y)=0
Thejoint PDFofabivariate RV (X,Y ) is given by fXY (x,y)= where k isaconstant. (a) Determine the value of k. (b) Find themarginal PDFsof X andY. (c) Find P(0<X <1/2,0<Y <1/2). (d) Findtheconditional PDFs fY|X(y|x) and fX|Y (x|y). (e) Computetheconditional meansE[Y |x] andE[X|y]. (f) Computetheconditional variancesVar(Y |x) andVar(X|y). otherwise { k, 0<y≤x<1, 0, otherwise, Thejoint PDFofabivariate RV (X,Y ) is given by fXY (x,y)= { k, 0<y≤x<1, 0, otherwise, where k isaconstant. (a) Determine the value of k. (b) Find themarginal...
Find fxx, fxy, fyx, and fy for the following function. (Remember, fyx means to differentiate with respect to y and then with respect to x.) f(x, y) = e9xy ロロロ
a. Given the joint probability den- sity function fxy(x, y) as, Skxy, (x, y) e shaded area Jxy(, 9) = 10 otherwise Find [i] k [ii] fx(x) [iii] fy(y) Are X and Y independent? b. Given the joint probability density function fxy(x, y) as, fxy(x, y) = { 0 kxy, (x, y) E shaded area otherwise Find [i] k [ii] fx(x) [iii] fy(y) Are X and Y independent? 2 1
Find fxx(x,y), fxy(x,y), fyx(x,y) and fyy(x,y) for the following
function.f(x,y)=5x2y2+3x6+4y
= xe +1),0 x, y < o. 1/(1y)2. 1. Let X, Y be jointly continuous with joint pdf f(x, y) The marginal densities of X, Y are fx(x)= e", fy (y) (a) (2 points) What are fxy(xy) and fyx(ylx)? (b) (3 points) Compute g(y) E(X[Y = y) and h(a) = E(Y|X = x). (c) (3 points) Compute E(XIY) and E(E(X|Y)) (d) (2 points) Check your answer from (c) by using E(X) E(E(XY) and computing E(X) = afx(x)da separately.
Let (X, Y) have joint pdf given by f(r, y)= < a, 0 < < 0, О.w., (a) Find the constant c (b) Find fx(x) and fy(y) (c) For 0 x< 1, find fyx=r (y) and py|x=x and oyx= (d) Find Cov(X, Y) (e) Are X and Y independent? Explain why
(II) Multiple continuous random variables: 8.2 Let X and Y have joint density fXY(x,y) = cx^2y for x and y in the triangle defined by 0 < x < 1, 0 < y < 1, 0 < x + y < 1 and fXY(x,y) = 0 elsewhere. a. What is c? b. What are the marginals fX(x) and fY(y)? c. What are E[X], E[Y], Var[X] and Var[Y]? d. What is E[XY]? Are X and Y independent?