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3. (30pt) Suppose that E(Y) = 1, E(Y2) = 2, E(Y3) = 3, V(Y1) = 6,...
2. [x] Suppose that Y1, Y2, Y3 denote a random sample from an exponential distribution whose...
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) =...
= = 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) =...
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 =...
1. Suppose we have three random variables Y1 , Y2 , and Y3 . Suppose we...
1. Suppose we have three random variables Y1 , Y2 , and Y3 .
Suppose we have three random variables Y, Y,, and Y,. The standard deviations of Y and Y, are both 3 and the standard deviation of Y is 2. The correlation coefficient between Y and Y, is-0.6. The covariance between Y and Y, is 0.5. Y is independent of Y 1. 1 2 a) (3 pts) Find Var(h + 3%) b) (3 pts) Find Cov(3h + 2⅓'5½-%)
2. Suppose the variables Y1 and Y2 have the following properties: 2. Suppose the variables Yi...
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%
Suppose two random variables Y1 and Y2 have the following quantities: E(Y) = 3, E(Y/2) =...
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
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1...
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
1 3 4 9. Suppose the discrete random variables X and Y are jointly distributed according...
1 3 4 9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: Yl-1 0 1 0.1 0.1 0.1 0 0.2 0.1 0.2 0.1 0.1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. (11) b. Let W = X - Y. Compute E(W) and V(W). [4] 10. Let X be a continuous random variable with probability density function h(x) ce* r >...
Problem 4: Of ten police officers at a precinct, four are married, three have never married,...
Problem 4: Of ten police officers at a precinct, four are married, three have never married, and three are divorced. Three of the officers are to be selected for promotion. Let Y1 denote the number of married officers and Y2 denote the number of never-married officers among the three selected for promotion. Assume that the three officers are randomly selected from the ten available (1) Find the joint probability function of Yi and Y2. (2) Find the marginal probability distribution...
1. Suppose that E(X) E(Y) E(Z) 2 Y and Z are independent, Cov(X, Y) V(X) V(Z)...
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.
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 =...
1. Suppose we have three random variables Y1 , Y2 , and Y3 .
Suppose we have three random variables Y, Y,, and Y,. The standard deviations of Y and Y, are both 3 and the standard deviation of Y is 2. The correlation coefficient between Y and Y, is-0.6. The covariance between Y and Y, is 0.5. Y is independent of Y 1. 1 2 a) (3 pts) Find Var(h + 3%) b) (3 pts) Find Cov(3h + 2⅓'5½-%)
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%
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
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
1 3 4 9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: Yl-1 0 1 0.1 0.1 0.1 0 0.2 0.1 0.2 0.1 0.1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. (11) b. Let W = X - Y. Compute E(W) and V(W). [4] 10. Let X be a continuous random variable with probability density function h(x) ce* r >...
Problem 4: Of ten police officers at a precinct, four are married, three have never married, and three are divorced. Three of the officers are to be selected for promotion. Let Y1 denote the number of married officers and Y2 denote the number of never-married officers among the three selected for promotion. Assume that the three officers are randomly selected from the ten available (1) Find the joint probability function of Yi and Y2. (2) Find the marginal probability distribution...
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.
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