I need the solution of this asap.
Thanks
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I need the solution of this asap.
Thanks
7. Let X Nu, E), where u= 0...
7. Let X ~ N(u, E), where -- II 0 2 1 and 1 1 2...
7. Let X ~ N(u, E), where -- II 0 2 1 and 1 1 2 4 = 2 2 1 1 4 2 Let Y = X3 + X1 2X2 X₃ – X, i) What is the distribution of Y? ii) Which components of Y are independent of each other?
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 =...
(c) (20 pts.) Let X have a uniform distribution U(0, 2) and let the considiton; distribution...
(c) (20 pts.) Let X have a uniform distribution U(0, 2) and let the considiton; distribution of Y given X = x be U(0, x3) i. Determine f (x, y). Make sure to describe the support of f. ii. Calculate fy (y) iii. Find E(Y).
(5) Recall that X ~Uniform(10, 1,2,... ,n - 1)) if if k E (0, 1,2,... ,n -1, P(x k)0 otherwise (a...
(5) Recall that X ~Uniform(10, 1,2,... ,n - 1)) if if k E (0, 1,2,... ,n -1, P(x k)0 otherwise (a) Determine the MGF of such a random variable. (b) Let X1, X2, X3 be independent random variables with X1 Uniform(10,1)) X2 ~Uniform(f0, 1,2]) Xs~ Uniform(10, 1,2,3,4]). X3 ~ U x2 ~ Uniform(10, 1,2)) 13Uniform Find the laws of both Y1 X1 +2X2 +6X3 and Y2 15X1 +5X2 + X3. (c) What is the correlation coefficient of Yi and ½?...
I will show the whole task here. I need a solution for task C C. let...
I will show the whole task here. I need a solution for
task C
C. let F, G, and H be three n x n matrices. Solve the
following equation with consideration on X, when it is known that
matrix F – G2 is invertible.
F(F+X) = G2(X+H)
5. let t and r be two parameters. a. Write the equationssystem X-S=-X3 3x3 + 3x1 = -X2 rX3 + x2 = X1 On the form: i) A x= ii) 7. x1...
I don't understand a iii and b ii, What's the procedure of deriving the limit distribution? Thanks. 6. Extreme...
I don't understand a iii and b ii, What's the procedure of
deriving the limit distribution? Thanks.
6. Extreme values are of central importance in risk management and the following two questions provide the fundamental tool used in the extreme value theory. (a) Let Xi,... , Xn be independent identically distributed (i. i. d.) exp (1) random variables and define max(Xi,..., Xn) (i) Find the cumulative distribution of Zn (ii) Calculate the cumulative distribution of Vn -Zn - Inn (iii)...
(7) 15 ptsl Let Y - a +bX +U, where X and U d b are...
(7) 15 ptsl Let Y - a +bX +U, where X and U d b are are randon variables and a an constants. Assume that E[U|X] 0 and Var u|X] - X2. (a) Is Y a random variable? Why? (b) Is U independent of X? Why? (c) Show that Eu0 and Var[uEX2] (d) Show that E[Y|X- a bX, and that E[Y abEX]. (e) Show that VarlyX] = X2, and that Varly-p?Var(X) + EX2].
and let (b) Let X, X,...,X, be a random sample form the normal distribution Nu,o) Σ-...
and let (b) Let X, X,...,X, be a random sample form the normal distribution Nu,o) Σ- ΣΧ be the sample mean, S2 be the sample variance. j-1 n-1 Σ--Σ( - 1' -nΣΤ-β). (i) Prove that Using it, determine the distribution of X (ii) Find the m.g.f. of X. n ΣT- ) Σ- 7 7 n (iii) Indicate the distributions ofJ 2 , respectively. and (iii) Given that X and S are independent, derive the m.g.f of (n-15, and then, σ'...
Week 7: Nonlinear equations 1. Let f(x) --9. The equation (x)0 has a solution in [0, 1] i) Find t...
Week 7: Nonlinear equations 1. Let f(x) --9. The equation (x)0 has a solution in [0, 1] i) Find the interpolation polynomial that interpolates f at x,-0, x2 1 0.5 and x3-1. ii) Use this polynomial to find an approximation to the solution of the equation f(x)0
Week 7: Nonlinear equations 1. Let f(x) --9. The equation (x)0 has a solution in [0, 1] i) Find the interpolation polynomial that interpolates f at x,-0, x2 1 0.5 and x3-1. ii)...
Please, I need solution of this asap. I will rate you high if you give correct...
Please, I need solution of this asap.
I will rate you high if you give correct solution
4. Let UX and V~xbe independent, and s > 2. i) Compute E (H] ii) Suppose T has a t-distribution with degree of freedom s > 2. Compute E[T) and Var(T). (Hint: use i) to find E [T?]).
7. Let X ~ N(u, E), where -- II 0 2 1 and 1 1 2 4 = 2 2 1 1 4 2 Let Y = X3 + X1 2X2 X₃ – X, i) What is the distribution of Y? ii) Which components of Y are independent of each other?
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 =...
(c) (20 pts.) Let X have a uniform distribution U(0, 2) and let the considiton; distribution of Y given X = x be U(0, x3) i. Determine f (x, y). Make sure to describe the support of f. ii. Calculate fy (y) iii. Find E(Y).
(5) Recall that X ~Uniform(10, 1,2,... ,n - 1)) if if k E (0, 1,2,... ,n -1, P(x k)0 otherwise (a) Determine the MGF of such a random variable. (b) Let X1, X2, X3 be independent random variables with X1 Uniform(10,1)) X2 ~Uniform(f0, 1,2]) Xs~ Uniform(10, 1,2,3,4]). X3 ~ U x2 ~ Uniform(10, 1,2)) 13Uniform Find the laws of both Y1 X1 +2X2 +6X3 and Y2 15X1 +5X2 + X3. (c) What is the correlation coefficient of Yi and ½?...
I will show the whole task here. I need a solution for
task C
C. let F, G, and H be three n x n matrices. Solve the
following equation with consideration on X, when it is known that
matrix F – G2 is invertible.
F(F+X) = G2(X+H)
5. let t and r be two parameters. a. Write the equationssystem X-S=-X3 3x3 + 3x1 = -X2 rX3 + x2 = X1 On the form: i) A x= ii) 7. x1...
I don't understand a iii and b ii, What's the procedure of
deriving the limit distribution? Thanks.
6. Extreme values are of central importance in risk management and the following two questions provide the fundamental tool used in the extreme value theory. (a) Let Xi,... , Xn be independent identically distributed (i. i. d.) exp (1) random variables and define max(Xi,..., Xn) (i) Find the cumulative distribution of Zn (ii) Calculate the cumulative distribution of Vn -Zn - Inn (iii)...
(7) 15 ptsl Let Y - a +bX +U, where X and U d b are are randon variables and a an constants. Assume that E[U|X] 0 and Var u|X] - X2. (a) Is Y a random variable? Why? (b) Is U independent of X? Why? (c) Show that Eu0 and Var[uEX2] (d) Show that E[Y|X- a bX, and that E[Y abEX]. (e) Show that VarlyX] = X2, and that Varly-p?Var(X) + EX2].
and let (b) Let X, X,...,X, be a random sample form the normal distribution Nu,o) Σ- ΣΧ be the sample mean, S2 be the sample variance. j-1 n-1 Σ--Σ( - 1' -nΣΤ-β). (i) Prove that Using it, determine the distribution of X (ii) Find the m.g.f. of X. n ΣT- ) Σ- 7 7 n (iii) Indicate the distributions ofJ 2 , respectively. and (iii) Given that X and S are independent, derive the m.g.f of (n-15, and then, σ'...
Week 7: Nonlinear equations 1. Let f(x) --9. The equation (x)0 has a solution in [0, 1] i) Find the interpolation polynomial that interpolates f at x,-0, x2 1 0.5 and x3-1. ii) Use this polynomial to find an approximation to the solution of the equation f(x)0
Week 7: Nonlinear equations 1. Let f(x) --9. The equation (x)0 has a solution in [0, 1] i) Find the interpolation polynomial that interpolates f at x,-0, x2 1 0.5 and x3-1. ii)...
Please, I need solution of this asap.
I will rate you high if you give correct solution
4. Let UX and V~xbe independent, and s > 2. i) Compute E (H] ii) Suppose T has a t-distribution with degree of freedom s > 2. Compute E[T) and Var(T). (Hint: use i) to find E [T?]).
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