Let Y, and Y, have the joint density function Se-(1 + Y2), y1 > 0, Y2 > 0, lo, f(y1, Y2) = elsewhere. (a) What is P(Y, < 7, Y2 > 8)? (Round your answer to four decimal places.) (b) What is P(Y, + Y, < 8)? (Round your answer to four decimal places.)

Q: The joint pdf of X and Y is given by fx,y(x,y) = {4x2   0<y<x<1}…

A: ANSWER: To determine the basis of a random variable U, we need to find the range of values ​​that U…

Q: The joint pdf of X and Y is given by fx,y(x,y) = {4x2   0<y<x<1}…

A: Sol:- To find the support of U, we first need to find the range of values that U can take

Q: Let f(x,y) = and let g(x, y) 4xy¹ 4x4 + 4y4 0 if(x, y) = (0,0) 0 if (x, y) = (0,0) 5xy 10 5x² + 5y20…

A: f(x,y)=4xy44x4+4y4if (x,y)≠(0,0)0if (x,y)=(0,0)g(x,y)=5xy105x2+5y20if (x,y)≠(0,0)0if (x,y)=(0,0)

Q: The joint pdf of X and Y is given by fxy(x, y) =e (x+y), x>0, y>0 ind the pdf of U: X + Y 2

A: The joint pdf of X and Y is,It is required to find the pdf of A joint pdf for two variables…

Q: Let f(x, y) = and let g(x, y) O O rºy6 26+y6 O 0 0 6x³y³ 6x6 + 6y6 Which of the above functions are…

A: fx,y=x6y6x6+y6if x,y≠0,00if x,y=0,0 gx,y=6x3y36x6+6y6if x,y≠0,00if x,y=0,0

Q: The population in a certain city has radial density function ρ(r) = 15(1 + r2)−1/2, where r is the…

A:

Q: p(x,y,z)=xz²+sin(y) ex e*

A:

Q: Find the gradient of f(x, y, z) =e^y cos(xz) at (1,0,1) .

A:

Q: Let f(x, y) and let g(x, y) = O O 8xy8 828+8y8 O 3xy6 3x² + 3y¹2 Which of the above functions are…

A:

Q: 1) Let f(x,y) = 6x,0 < x < y<1 and 0 elsewhere. Find a) The marginal density of X and Y

A: The provided information is  f(x,y)=6x    0&lt;x&lt;y&lt;1   and 0 otherwise Therefore  a. The…

Q: The population density of a city is approximated by the model f(x, y) = 2000e−0.01(x2 + y2), x2 +…

A:

Q: X~U(0,1)  and Y|X = x~U(x,1) a) what is joint pdf fX,Y(x,y)? b) what is marginal pdf fY(y)? c)…

A: Given, X~U(0,1)  and Y|X = x~U(x,1)

Q: Astroid: (0 s t s 2x) x = a cos3 t y = a sin3 t a ab 3 o 2ra2 O zab 2nab

A: