Homework Answers
SOLUTION:
Given that,
X,Y have a bivariate normal distribution
marginal distribution X (0,1)
conditional distribution of Y given X = x is
(ax +b,
).
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6. Suppose X, Y have a bivariate normal distribution with marginal dis- tribution...
6. Suppose that (W, Z) have a bivariate normal distribution, that W ∼ N (0, 1),...
6. Suppose that (W, Z) have a bivariate normal distribution,
that W ∼ N (0, 1), and that the conditional distribution of Z,
given that W = w, is N (aw + b, τ 2 ). (a) What is the marginal
distribution of Z? (b) What is the conditional distribution of W,
given that Z = z?
6. Suppose that (W, Z) have a bivariate normal distribution, that W N(0,1), and that the conditional distribution of Z, given that W-w....
Suppose that (W,Z) have a bivariate normal distribution, that W ~N(0,1), and that the conditional distribution...
Suppose that (W,Z) have a bivariate normal distribution, that W ~N(0,1), and that the conditional distribution of Z, given that Ww, is N(aw b,T2). (a) What is the marginal distribution of Z? (b) What is the conditional distribution of W, given that Z2?
6. Suppose that (W, Z) have a bivariate normal distribution, that W~N(0, 1), and that the...
6. Suppose that (W, Z) have a bivariate normal distribution, that W~N(0, 1), and that the conditional distribution of Z, given that W-w, is N(aw b, T2). (a) What is the marginal distribution of Z? b) What is the conditional distribution of W, given that Z-2?
The random variables Z and W have a bivariate normal dis- tribution with EZ] = E[W] = 0, Var(Z) =...
The random variables Z and W have a bivariate normal dis- tribution with EZ] = E[W] = 0, Var(Z) = Var(W) = 1, and oorrelation ρ E (-1,1). Given that Pl2+ W 1-8413, find the value ofp. Hint: 8413 = φ(1), where φ is the standard normal distribution function.]
The random variables Z and W have a bivariate normal dis- tribution with EZ] = E[W] = 0, Var(Z) = Var(W) = 1, and oorrelation ρ E (-1,1). Given that Pl2+...
please help me 5. Suppose X and Y are standard normal random variables. Find an expres-...
please help me
5. Suppose X and Y are standard normal random variables. Find an expres- sion for P(X - 3Y S1) in terms of the standard normal distribution function In two cases: (i) X and Y are independent (ii) X and Y have bivariate normal distribution with correlation ρ-1/2.
6. Suppose that X and Y have a bivariate normal distribution with px 1 and y- (a) Order the follo...
6. Suppose that X and Y have a bivariate normal distribution with px 1 and y- (a) Order the following probabilities from largest to smallest, assuming p >0: P(X 2 (b) Repeat (a) assuming p < 0. (c) Repeat (a) assuming we are interested in (X 0.25) instead of (x 2 2).
6. Suppose that X and Y have a bivariate normal distribution with px 1 and y- (a) Order the following probabilities from largest to smallest, assuming p >0:...
Suppose (X, Y ) has bivariate normal distribution, E(X) = E(Y ) = 0,V ar(X) =...
Suppose (X, Y ) has bivariate
normal distribution, E(X) = E(Y ) = 0,V ar(X) = σX2 , V ar(Y ) =
σY2 and Correl(X, Y ) = ρ. Calculate the conditional expectation
E(X2|Y ).
I. Suppose (X,Y) has bivariate normal distribution, E(X) = E(Y) 0, Var(X)-σ , Var(Y) σ and Correl (X,Y)-p. Calculate the conditional expectation ECKY expectation E(X2Y)
bos on 559 2. Random variable X and Y have a bivariate normal distribution. The conditional...
bos on 559 2. Random variable X and Y have a bivariate normal distribution. The conditional density of X given Y = y is a OVH a. bivariate normal distribution Bossiu b. chi-square distribution c. linear distribution oms d. normal distribution e. not necessarily any of the above distributions. 3. The probability distribution for the random variable X is shown by the table. Use the transformation technique to construct the table for the probability distribution of Y = x2 +...
1. Suppose (x, Y) has bivariate normal distribution, E(x) E(Y)- 0, Var(X) σ , Var(Y) σ...
1. Suppose (x, Y) has bivariate normal distribution, E(x) E(Y)- 0, Var(X) σ , Var(Y) σ and Correl(X, Y) p. Calculate the conditional expectation E(X2|Y).
17. Suppose that (X,Y) has a bivariate normal distribu- zion with parameters diy, x, 0y.p. io...
17. Suppose that (X,Y) has a bivariate normal distribu- zion with parameters diy, x, 0y.p. io show that (2 , 4") has a bivariate normal distri- bution with parameters 0, 1,0.1.p. b) What is the joint distribution of (aX + b,cY + d).
6. Suppose that (W, Z) have a bivariate normal distribution,
that W ∼ N (0, 1), and that the conditional distribution of Z,
given that W = w, is N (aw + b, τ 2 ). (a) What is the marginal
distribution of Z? (b) What is the conditional distribution of W,
given that Z = z?
6. Suppose that (W, Z) have a bivariate normal distribution, that W N(0,1), and that the conditional distribution of Z, given that W-w....
Suppose that (W,Z) have a bivariate normal distribution, that W ~N(0,1), and that the conditional distribution of Z, given that Ww, is N(aw b,T2). (a) What is the marginal distribution of Z? (b) What is the conditional distribution of W, given that Z2?
6. Suppose that (W, Z) have a bivariate normal distribution, that W~N(0, 1), and that the conditional distribution of Z, given that W-w, is N(aw b, T2). (a) What is the marginal distribution of Z? b) What is the conditional distribution of W, given that Z-2?
The random variables Z and W have a bivariate normal dis- tribution with EZ] = E[W] = 0, Var(Z) = Var(W) = 1, and oorrelation ρ E (-1,1). Given that Pl2+ W 1-8413, find the value ofp. Hint: 8413 = φ(1), where φ is the standard normal distribution function.]
The random variables Z and W have a bivariate normal dis- tribution with EZ] = E[W] = 0, Var(Z) = Var(W) = 1, and oorrelation ρ E (-1,1). Given that Pl2+...
please help me
5. Suppose X and Y are standard normal random variables. Find an expres- sion for P(X - 3Y S1) in terms of the standard normal distribution function In two cases: (i) X and Y are independent (ii) X and Y have bivariate normal distribution with correlation ρ-1/2.
6. Suppose that X and Y have a bivariate normal distribution with px 1 and y- (a) Order the following probabilities from largest to smallest, assuming p >0: P(X 2 (b) Repeat (a) assuming p < 0. (c) Repeat (a) assuming we are interested in (X 0.25) instead of (x 2 2).
6. Suppose that X and Y have a bivariate normal distribution with px 1 and y- (a) Order the following probabilities from largest to smallest, assuming p >0:...
Suppose (X, Y ) has bivariate
normal distribution, E(X) = E(Y ) = 0,V ar(X) = σX2 , V ar(Y ) =
σY2 and Correl(X, Y ) = ρ. Calculate the conditional expectation
E(X2|Y ).
I. Suppose (X,Y) has bivariate normal distribution, E(X) = E(Y) 0, Var(X)-σ , Var(Y) σ and Correl (X,Y)-p. Calculate the conditional expectation ECKY expectation E(X2Y)
bos on 559 2. Random variable X and Y have a bivariate normal distribution. The conditional density of X given Y = y is a OVH a. bivariate normal distribution Bossiu b. chi-square distribution c. linear distribution oms d. normal distribution e. not necessarily any of the above distributions. 3. The probability distribution for the random variable X is shown by the table. Use the transformation technique to construct the table for the probability distribution of Y = x2 +...
1. Suppose (x, Y) has bivariate normal distribution, E(x) E(Y)- 0, Var(X) σ , Var(Y) σ and Correl(X, Y) p. Calculate the conditional expectation E(X2|Y).
17. Suppose that (X,Y) has a bivariate normal distribu- zion with parameters diy, x, 0y.p. io show that (2 , 4") has a bivariate normal distri- bution with parameters 0, 1,0.1.p. b) What is the joint distribution of (aX + b,cY + d).
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