1.
X ~ N(mu = 3,sigma=10)
Y=2X+4
E(Y) = ?
2.
X ~ N(mu = 3,sigma=10)
Y=2X+4
V(Y) = ?
3.
If X and Y are independent then E(XY) =E(X)*E(Y)
True or False?
4.
If Cov(X,Y) = 0 then X and Y are independent
True or False?
5.
If Y_1 ~ N( 1, sigma =2) and Y_2 ~ N(-2, sigma^2 = 16) and Y_1 is independent of Y_2.
If l = 2Y_1 - 3Y_2 find E(l)
6.
If Y_1 ~ N( 1, sigma =2) and Y_2 ~ N(-2, sigma^2 = 16) and Y_1 is independent of Y_2.
If l = 2Y_1 - 3Y_2 find V(l)
1. X ~ N(mu = 3,sigma=10) Y=2X+4 E(Y) = ? 2. X ~ N(mu = 3,sigma=10)...
1. Suppose that E(X) E(Y) E(Z) 2 Y and Z are independent, Cov(X, Y) V(X) V(Z) 4, V(Y) = 3 Let U X 3Y +Z and W = 2X + Y + Z 1, and Cov(X, Z) = -1 Compute E(U) and V (U) b. Compute Cov(U, W). а.
Problem 2 Suppose two continuous random variables (X, Y) ~ f(x,y). (1) Prove E(X +Y) = E(X)+ E(Y). (2) Prove Var(X + Y) = Var(X) + Var(Y)2Cov(X, Y). (3) Prove Cov(X, Y) E(XY)- E(X)E(Y). (4) Prove that if X and Y are independent, i.e., f(x, y) Cov(X, Y) 0. Is the reverse true? (5) Prove Cov (aX b,cY + d) = acCov(X, Y). (6) Prove Cov(X, X) = Var(X) fx (x)fy(y) for any (x,y), then =
X
and z are independent. Var(x)=1 ; Var(z) = sigma ^2. E(z)= 0 and y=
ax+b+z
I) cov(x,y)= ?
ii) corr(x,y)=?
dependent Varvane 2.
4. Recall that the covariance of random variables X, and Y is defined by Cov(X,Y) = E(X - Ex)(Y - EY) (a) (2pt) TRUE or FALSE (circle one). E(XY) 0 implies Cov(X, Y) = 0. (b) (4 pt) a, b, c, d are constants. Mark each correct statement ( ) Cov(aX, cY) = ac Cov(X, Y) ( ) Cor(aX + b, cY + d) = ac Cov(X, Y) + bc Cov(X, Y) + da Cov(X, Y) + bd ( )...
1) given mu = 20 and sigma = 3 a) probability(x<18) b)probability(x>21) 2) given mu = 50 and sigma = 4 a) find 90% confidence interval b) find 94%
1. Let X ~ Bin(n = 12, p = 0.4) and Y Bin(n = 12, p = 0.6), and suppose that X and Y are independent. Answer the following True/False questions. (a) E[X] + E[Y] = 12. (b) Var(X) = Var(Y). (c) P(X<3) + P(Y < 8) = 1. (d) P(X < 6) + P(Y < 6) = 1. (e) Cov(X,Y) = 0.
Assume X, Y are independent with EX = 1 EY = 2 Var(X) = 22 Var(Y) = 32 Let U = 2X + Y and V = 2X – Y. (a) Find E(U) and E(V). (b) Find Var(U) and Var(V). (c) Find Cov(U,V).
Let xi be independent. E(xi)=0. Var(xi)= sigma ^2
Cov(x,y) = E(XY) - ExEy
Use this fact and apply it to this example ! Do not use
anything that has not been giving. I’m having difficulties
completing this problem. Check pictures to see how I done a
far
AaBbCcDdEe AaBbCc Normal No Spac hoose Check for Updates. に1 に2 We were unable to transcribe this image
Y=2x+1, find the pmf of y ,E(y) and var(y)
Zhejiang University of Science and Technology 2. The joint pmf of X and Y is 2 6 0 4 0 Find the marginal distribution of Y and E(XY).
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