Homework Answers
Let f(x, y) = x2 – yż and D= {(2,y) : x2 + y2 < 4}....
Let f(x, y) = x2 – yż and D= {(2,y) : x2 + y2 < 4}. Let m and M be the absolute minimum and maximum values of f over D respectively. What is m - M?
5.Use polar coordinates system to evaluate: x2 + y2)dydx , R is the region enclosed by...
5.Use polar coordinates system to evaluate: x2 + y2)dydx , R is the region enclosed by 0 <x< 1 and, -x sy sx
1. Let X and Y be random variables with joint probability density function flora)-S 1 (2...
1. Let X and Y be random variables with joint probability density function flora)-S 1 (2 - xy) for 0 < x < 1, and 0 <y <1 elsewhere Find the conditional probability P(x > ]\Y < ).
(7 pts.) Let f(x, y, z) = "y and let R be the region {(x, y,...
(7 pts.) Let f(x, y, z) = "y and let R be the region {(x, y, z) |2 < x < 4,0 Sy < 3,15 zse}. 2 Evaluate | $180,0,.2) av. R
2. Let the random variables Y1 and Y, have joint density Ayſy22 - y2) 0<yi <1,...
2. Let the random variables Y1 and Y, have joint density Ayſy22 - y2) 0<yi <1, 0 < y2 < 2 f(y1, y2) = { otherwise Stom.vn) = { isiml2 –») 05451,05 ms one a independent, amits your respon a) Are Y1 and Y2 independent? Justify your response. b) Find P(Y1Y2 < 0.5). on the
2. (10 pts The random variables X and Y have joint density function f(x, y) ==...
2. (10 pts The random variables X and Y have joint density function f(x, y) == 22 + y2 <1. Compute the joint density function of R= x2 + y2 and = tan-1(Y/X).
Let f left parenthesis x comma y right parenthesis equals x squared plus y squared minus...
Let f left parenthesis x comma y right parenthesis equals x
squared plus y squared minus 2 y plus 1 and let R colon x squared
plus y squared less or equal than space 4, shown below
Let f(x,y) = x2 + y2 – 2y +1 and let R:x2 + y2 < 4, shown below. + Find the absolute extrema for f on R. f has an absolute maximum value of f has an absolute minimum value of **You only...
Let X and Y be random variables with joint PDF fx,y(x, y) = 2 for 0...
Let X and Y be random variables with joint PDF fx,y(x, y) = 2 for 0 < y < x < 1. Find Var(Y|X).
Let X,Y be uniformly distributed in the rectangle defined by −3 < x−y < 3, 1...
Let X,Y be uniformly distributed in the rectangle defined by −3
< x−y < 3, 1 < x + y < 5. Find the marginal density
fX(x) and E(Y|X).In the same situation find Cov(X,Y ).
(3) Let X, Y be uniformly distributed in the rectangle defined by -3 < x-y<3, Find the marginal density fx(x) and E(Y|X). In the same situation find Cov(X, Y). 1<x+y<5.
f a random sample X,X, X, from the 2. Let Y, < Y.< Y, be the...
f a random sample X,X, X, from the 2. Let Y, < Y.< Y, be the order statistics o exponential distribution with mean β. Let (i) Are the random variables U,V,W independent? (ii) What is the distribution of each of U,V and W.
Let f(x, y) = x2 – yż and D= {(2,y) : x2 + y2 < 4}. Let m and M be the absolute minimum and maximum values of f over D respectively. What is m - M?
5.Use polar coordinates system to evaluate: x2 + y2)dydx , R is the region enclosed by 0 <x< 1 and, -x sy sx
1. Let X and Y be random variables with joint probability density function flora)-S 1 (2 - xy) for 0 < x < 1, and 0 <y <1 elsewhere Find the conditional probability P(x > ]\Y < ).
(7 pts.) Let f(x, y, z) = "y and let R be the region {(x, y, z) |2 < x < 4,0 Sy < 3,15 zse}. 2 Evaluate | $180,0,.2) av. R
2. Let the random variables Y1 and Y, have joint density Ayſy22 - y2) 0<yi <1, 0 < y2 < 2 f(y1, y2) = { otherwise Stom.vn) = { isiml2 –») 05451,05 ms one a independent, amits your respon a) Are Y1 and Y2 independent? Justify your response. b) Find P(Y1Y2 < 0.5). on the
2. (10 pts The random variables X and Y have joint density function f(x, y) == 22 + y2 <1. Compute the joint density function of R= x2 + y2 and = tan-1(Y/X).
Let f left parenthesis x comma y right parenthesis equals x
squared plus y squared minus 2 y plus 1 and let R colon x squared
plus y squared less or equal than space 4, shown below
Let f(x,y) = x2 + y2 – 2y +1 and let R:x2 + y2 < 4, shown below. + Find the absolute extrema for f on R. f has an absolute maximum value of f has an absolute minimum value of **You only...
Let X and Y be random variables with joint PDF fx,y(x, y) = 2 for 0 < y < x < 1. Find Var(Y|X).
Let X,Y be uniformly distributed in the rectangle defined by −3
< x−y < 3, 1 < x + y < 5. Find the marginal density
fX(x) and E(Y|X).In the same situation find Cov(X,Y ).
(3) Let X, Y be uniformly distributed in the rectangle defined by -3 < x-y<3, Find the marginal density fx(x) and E(Y|X). In the same situation find Cov(X, Y). 1<x+y<5.
f a random sample X,X, X, from the 2. Let Y, < Y.< Y, be the order statistics o exponential distribution with mean β. Let (i) Are the random variables U,V,W independent? (ii) What is the distribution of each of U,V and W.
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