1. Suppose we have three random variables Y1 , Y2 , and Y3 .
1.
a)
General formula for Variance of sum of two random variables X and Y is :
We need to find,
We know that,
So,
We are also given,
Formula for correlation between two Random variables X and Y is :
So,
So,
b)
Now, we need to find,
Since, Y2 and Y3 are independent , so ,
and we also have,
Putting all the values we get,
1. Suppose we have three random variables Y1 , Y2 , and Y3 . Suppose we...
2. Suppose the variables Y1 and Y2 have the following properties: 2. Suppose the variables Yi and Y2 have the following properties: E(%) = 4, Var(%) = 19,E(%) = 6.5, Var(%) = 5.25,E(,%) = 30 Calculate the following; please show the underlying work: a) (3 pts) Cov(Y,Y2) b) (3 pts) Cov(4Y1,3Y2) c) (3 pts) Cov(4h, 5-½) d) (6 pts) Find the correlation coefficient between 1 + 3, and 3-2%
3. (30pt) Suppose that E(Y) = 1, E(Y2) = 2, E(Y3) = 3, V(Y1) = 6, V(Y2) = 7,V (Y3) = 8, Cov(Yı, Y2) = 0, Cov(Yı, Y3) = -4 and 10 1 2 3 Cov(Y2, Y3) = 5. Also define a = 20 and A = 4 5 6 30/ ( 7 8 9 (a) (10pt) Find the expected value and variance covariance matrix of Y, where Y = Y2 (b) (10pt) Compute Eſa'Y) and E(AY). (c) (10pt) Compute...
Suppose two random variables Y1 and Y2 have the following quantities: E(Y) = 3, E(Y/2) = 18, E(Y2) = 5, E(Y22) = 29, E(Y1Y2) = 11 Find the correlation coefficient of Y1 and Y2. That is to find the value of Corr(Y 1, Y2) -4.0000 0.6667 O -0.1111 -0.6667
2. Suppose the variables Yi and Y have the following properties EQİ)-4, Var(h)-19, E(Y )-6.5, Var(Ya)-5.25, E(Y3%)-30 Calculate the following; please show the underlying work a) (3 pts) Cov(, ) b) (3 pts) Cov(41, 3%) c) (3 pts) Cov(41.5-½) (6 pts) Find the correlation coefficient between 1 + 3, and 3-2%
Let Y1, Y2, and Y3 be independent, N(0, 1)-distributed random variables, and set X1 = Y1 − Y3, X2 = 2Y1 + Y2 − 2Y3, X3 = −2Y1 + 3Y3.Determine the conditional distribution of X2 given that X1 + X3 = x.
2. [x] Suppose that Y1, Y2, Y3 denote a random sample from an exponential distribution whose pdf and cdf are given by f(y) = (1/0)e¬y/® and F(y) =1 – e-y/0, 0 > 0. It is also known that E[Y;] = 0. ', y > 0, respectively, with some unknown (a) Let X = min{Y1,Y2, Y3}. Show that X has pdf given by f(æ) = (3/0)e-3y/º. Start by thinking about 1- F(x) = Pr(min{Y1,Y2, Y3} > x) = Pr(Y1 > x,...
= = 3, Cov(X1, X2) = 2, Cov(X2, X3) = -2, Let Var(X1) = Var(X3) = 2, Var(X2) Cov(X1, X3) = -1. i) Suppose Y1 = X1 - X2. Find Var(Y1). ii) Suppose Y2 = X1 – 2X2 – X3. Find Var(Y2) and Cov(Yı, Y2). Assuming that (X1, X2, X3) are multivariate normal, with mean 0 and covariances as specified above, find the joint density function fxı,Y,(y1, y2). iii) Suppose Y3 = X1 + X2 + X3. Compute the covariance...
I need the solution of this question asap 3, Cov(X1, X2) = 2, Cov(X2, X3) = -2, 5. Let Var(x1) = Var(X3) = 2, Var(X2) Cov(X1, X3) = -1. i) Suppose Y1 = X1 - X2. Find Var(Y1). ii) Suppose Y2 = X1 – 2X2 – X3. Find Var(Y2) and Cov(Y1, Y2). Assuming that (X1, X2, X3) are multivariate normal, with mean 0 and covariances as specified above, find the joint density function fyy, y,(91, y2). iii) Suppose Y3 =...
14. Random variables X and Y have a density function f(x, y). Find the indicated expected value. f(x, y) = (xy + y2) 0<x< 1,0 <y<1 0 Elsewhere {$(wyty E(x2y) = 15. The means, standard deviations, and covariance for random variables X, Y. and Z are given below. LIX = 3. HY = 5. Az = 7 Ox= 1, = 3, oz = 4 cov(X,Y) = 1, cov (X, Z) = 3, and cov (Y,Z) = -3 T = X-2...
Show steps, thanks ·Additional Problem 13. For random variables X and Y it is given that Ox = 2, ơY = 5, and pxy 3 (a) Find Cov(Xx,y) (b) Var(4X-2Y7 Answers: (a) -. (b) 002 10652 li 3 . Additional Problem 14. Suppose Xi and X2 are independent random variables that have exponential distribution with β 4. (a) Find the covariance and correlation between 5Xi + 3X, and 7Xi-2X. (b) Find Var-5X2-2