suppose E[X]=2 and E[Y]=1. can we calculate E[XY]? explain why or why not?
E[XY] = E(X)*E(Y)
Only if it is given that X any Y are independent of each other.
Then,
E[XY] = 2*1 = 2
But in case they are not independent then the above solution will be incorrect.
Ex:- For not independent event(attached file)
suppose E[X]=2 and E[Y]=1. can we calculate E[XY]? explain why or why not?
2. Suppose ElX) = 2 and EY-1 as in part 1. Can we calculate E(XY)? explain why or why not?
1. Consider the equation xy" - 2y' + (2 - x)y = 0,x > 0. We can easily verify that y(x) = e* is a solution of the equation. Use reduction of order to determine the general solution of the equation.
Suppose X ∼ N(0, 1). (1) Explain the density of X in terms of the diffusion process. (2) Calculate E(X), E(X^2 ), and Var(X). (3) Let Y = µ + σX. Calculate E(Y ) and Var(Y ). Find the density of Y.
Problem 4 Suppose X ~N(0, 1) (1) Explain the density of X in terms of diffusion process. (2) Calculate E(X), E(X2), and Var(X). (3) Let Y = μ +ơX. Calculate E(Y) and Var(Y). Find the density of Y.
Problem 4 Suppose X ~N(0, 1) (1) Explain the density of X in terms of diffusion process. (2) Calculate E(X), E(X2), and Var(X). (3) Let Y = μ +ơX. Calculate E(Y) and Var(Y). Find the density of Y.
Suppose E is the half-cylinder described by x^2 + y^2 = 1 between z = 4 and the xy-plane where y ≥ 0. Suppose further that the density at each point in E is proportional to the distance from the z-axis. (a) Find an expression for the mass of E as a triple integral. Then briefly explain why this integral is difficult to compute. (b) (8 points) Describe the solid E using cylindrical coordinates.Then express the mass of E as...
4. Suppose that X and Y are random variables with E(X) = 2, E(Y) = 1. E(X*) = 5, E(Y2-10, and E(XY) = 1 (a) Compute Corr(X,Y) (b) Choose a number c so that X and X +cY are uncorrelated
explain please
2. Which one of the following DE is exact? a. (x+y)dx+(xy+1) dy=0 b (e + y)<x+ſe+x)dy = 0 c.(ye* +1) dx +(e' + xy) dy = 0 d. (sin x+cos y) dx +(cos x +sin y) dy = 0 e. (eº+1) dx +(e? + 2) dy = 0 3. The solution of the following separable DE xy' =-y? is a. y= '+c b. y=- c. y = In x+c In x+c d. In y=x? + e. yer+C 4....
Suppose that f(x,y)=xy. Find the maximum value of the function if x and y are constrained to sum to 1. b) How can you be sure this is a maximum and not a minimum?
1. Suppose X and Y are continuous random variables with joint pdf f(x,y) 4(z-xy) if = 0 < x < 1 and 0 < y < 1, and zero otherwise. (a) Find E(XY) b) Find E(X-Y) (c) Find Var(X - Y) (d) What is E(Y)?
there is no need to introduce new variables
2. Consider a joint pdf Find: (a) E(X|Y = y). (b) E(Y|X =x). (c) E(XY)
2. Consider a joint pdf Find: (a) E(X|Y = y). (b) E(Y|X =x). (c) E(XY)