Exercise 9.2. Let Z~ N(0, 1). Find the variance of Z2 and Z3 N0 1) Find...

Question

Question

Answer 1

Answer #1

Solution: 2NNCO, 1) we know that ZONCO, 1) 28 NX Chi-squre with degrees of freedom E(20) = 1 and varience 22 = 2 var (22) = 2

Answer 2

Similar Homework Help Questions

1. Let Z = (Z1, Z2, Z3) be a vector with i.i.d. N(0, 1) components. Let...

1. Let Z = (Z1, Z2, Z3) be a vector with i.i.d. N(0, 1) components. Let r be a constant with 0 < r < 1. Define X1 = √ rZ1 + √ 1 − rZ2 and X2 = √ rZ1 + √ 1 − rZ3. (a) Give the distribution of X1 and the distribution of X2. Find Cov(X1, X2). (b) Give the matrix A so that the vector X = (X1, X2) is a transform X = AZ. Give...
Note: if z = (z1, z2, z3), then the vectors x = (−z2, z1, 0) and...

Note: if z = (z1, z2, z3), then the vectors x = (−z2, z1, 0) and y = (−z3, 0, z1) are both orthogonal to z. Consider the plane P = H4 (1,−1,3) in R 3 . Find vectors w, x, y so that P = w + Span(x, y). Note: if z = (2,22,23), then the vectors x = (-22,21,0) and y = (-23,0,2) are both orthogonal to z. Consider the plane P = H(1,-1,3) in R3. Find vectors...
Problem 2. (Conditional Distribution of MVN) Let Z1, Z2, Z3 be i.i.d. N(0,1) dis- tributed random...

Problem 2. (Conditional Distribution of MVN) Let Z1, Z2, Z3 be i.i.d. N(0,1) dis- tributed random variables, and set X1 = 21 – Z3 X2 = 2Z1 + Z2 – 223 X3 = -221 +3Z3 1) What distribution does X = (X1, X2, X3)T follow? Specific the parameters. 2) Find out P(X2 > 0|X1 + X3 = 0).

Let x[n] ←→ X(z) and let x[n] = αnu[n]. Let x1[n] ←→X(z3). Find x1[n] without computing...

Let x[n] ←→ X(z) and let x[n] = αnu[n]. Let x1[n] ←→X(z3). Find x1[n] without computing X(z) or using properties of the z-transform.
Let the sequence: x[n]= { (a^n)*sin(nw), a>0 known constant, n ∈ N0 else x[n]=0 Find with...

Let the sequence: x[n]= { (a^n)*sin(nw), a>0 known constant, n ∈ N0 else x[n]=0 Find with a direct calculation (without using the transformation matrix Z) the transform Z of x [n], its convergence pass, the roots (zeroes) and its poles.
Exercise 8.43. Let Z1, Z2,... . Zn be independent normal random variables with mean 0 and variance 1. Let (a) Using that Y is the sum of independent random variables, compute both the mean and varian...

Exercise 8.43. Let Z1, Z2,... . Zn be independent normal random variables with mean 0 and variance 1. Let (a) Using that Y is the sum of independent random variables, compute both the mean and variance of Y. (b) Find the moment generating function of Y and use it to compute the mean and variance of Y. Exercise 8.43. Let Z1, Z2,... . Zn be independent normal random variables with mean 0 and variance 1. Let (a) Using that Y...

Let U ⊂ C4 be the subspace U = {(z1, z2, z3, z4) ∈ C4: z1...

Let U ⊂ C4 be the subspace U = {(z1, z2, z3, z4) ∈ C4: z1 + z2 + z3 + z4 = 0 and z1 = iz2}. (a) Find a basis for U. What is dim U? (b) Extend the basis from part (a) to a basis for C4. (c) Find a subspace W ⊂ C4 such that C4 = U ⊕ W. What is dim W?
Let Z! = 3H4, Z2-5-2, Z,--3-12, Z4--10-j6, and Z5--6-3. 1. Calculate Z1 + Z2 in rectangular...

Let Z! = 3H4, Z2-5-2, Z,--3-12, Z4--10-j6, and Z5--6-3. 1. Calculate Z1 + Z2 in rectangular form. 2. Calculate Z1 - Z2 in rectangular form. 3. Calculate Z3 + Z4 in polar form. 4. Calculate Za - Z5 in polar form. 5. Calculate Z1Z2-Z3 in rectangular form. 6. Find ZsZ7 in polar form. 7. Find Z7Zs in rectangular form. 8. Find ZsZs+Z7 in rectangular form Reduce the following to rectangular form. 10. Z1/Z2
Let Z ~ N(0,1) and let Y = Z2. Find the distribution of Y. Hint: Use...

Let Z ~ N(0,1) and let Y = Z2. Find the distribution of Y. Hint: Use moment generating function. Let X ~ N(j = 1, 02 = 4). If Y = 0.5*, find E(Y?). Hint: Use moment generating function.

(i) Find a non-zero polynomial in Z3 x| which induces a zero function on Z3. f(x), g(x) R have degree n and let co, c1,...

(i) Find a non-zero polynomial in Z3 x| which induces a zero function on Z3. f(x), g(x) R have degree n and let co, c1,... , cn be distinct elements in R. Furthermore, let (ii) Let f(c)g(c) for all i = 0,1,2,...n. g(x) Prove that f(x - where r, s E Z, 8 ± 0 and gcd(r, s) =1. Prove that if x is a root of (iii) Let f(x) . an^" E Z[x], then s divides an. aoa1 (i)...