Find P(Y < 1/3 | X < 1/3)
given,
f(x,y) = (3/4)(x^2+3y^2) , 0 < x < 1, 0 < y < 1
Find P(Y < 1/3 | X < 1/3) given, f(x,y) = (3/4)(x^2+3y^2) , 0 < x...
3. Let y" +2y' - 3y = f(x). Find the solution in the cases (a) f(x)=0; (b) f(x) 6x; (c) f(x) = 4 , y(0)-0, y'(0) - 1.
3. Given f(x,y)= sin?(2x+3y?).e***; (a) Find f (x,y). (b) Find f (x,y).
Suppose X and Y have the joint pdf f (x, y) = 3y, 0 < y < 1, y − 1 < x < 1 − y 0 otherwise a) Give an expression for P (X > Y ). b) Find the marginal pdfs for Y . c) Find the conditional pdf of X given Y = y, where 0 < y < 1. d) Give an expression for E[XY ]. e) Are X and Y independent?
Find f (x,y). f(x,y)= e - 4x + 3y A. fx(x,y)= -4 e - 4x OB. {x(x,y)= - 4 € -4x+3y OC. fx(x,y) = e -4x+3 OD. fx(x,y) = 3 e - 4x+3y
0, otherwise Let f(x,y)= 3. Sketch the region of integration Find k. Find P(X |Y 1/4) Find P(X |Y=1/4) a. b. c. d.
4. Find k for which the function given by f(x, y) = P(X = x, Y = y) = kxy, for x = 1, 2, 3; y = 1,2,3, can serve as a joint probability distribution. [2 points) Also, determine the following: • F(2, 2). [2 points) • the marginal distribution of X; [2 points) • the marginal distribution of Y; [2 points] • P(X > 1, Y < 3). (2 points] • P(X = 1, Y <3). [2 points)
Suppose that f(x, y) = cx, for 0 y x 2. (a) Find c. (b) Find P(x > 1 and Y < (c) Find the marginal pdf of X. (d) Find the conditional pdf of Y given that X = x. (e) Find E[Y IX x (f) Find E[E[YX]]. (g) Find Cov(X, Y) (h) Are X and Y independent?
Suppose that f(x, y) = cx, for 0 y x 2. (a) Find c. (b) Find P(x > 1 and Y
4. Let 3 f(x, y, z) = x’yz-xyz3, 4 P(2, -1, 1), u =< 0, > 5 a). Find the gradient of f. b). Evaluate the gradient at the point P. c). Find the rate of change of f at the point of P in the direction of the vector u.
Given f(x,y) = [x*sqrt(y)] / 3224 , 0<x<y<5.76 (f(x,y)= 0 otherwise) Find P(x + y > 0.5 | x = 1/5)
The density f(x,y) is given by the formula f(x,y) = 8x(x + y), x ≥ 0, y ≥ 0, x + y ≤ 1 and zero otherwise. (a) Find the marginal distributions. (b) Find the conditional distribution of Y given X = x. (c) Find P(X ≤ 1/2, Y ≤ 1/2) (d) Find P(X ≤ 1/2) (e) Find P(Y ≤ 1/2 | X ≤ 1/2) (f) Find P(Y ≤ 1/2 | X = 1/2)