Question

Let X and Y be two random variables which follow standard normal distribution. Let J =...

Let X and Y be two random variables which follow standard normal distribution. Let J = X − Y . Find the distribution function of J. Also find E[J] and Var[J].

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let random variables X and Y follow a bivariate Gaussian distribution, where X and Y are...
Let random variables X and Y follow a bivariate Gaussian distribution, where X and Y are independent and Cov(X,Y) = 0. Show that Y|X ~ Normal(E[Y|X], V[Y|X]). What are E[Y|X] and V[Y|X]?
Let X and Y be random variables and c a constant. Let Z = X +...
Let X and Y be random variables and c a constant. Let Z = X + cY. You are given the following information: E(X) = 5, Var(X) = 10, E(Y) = 3, Var(Y) = 1, Var(Z) = 37, and Cov(X,Y)=3. Find c if E(Z)≥0.
6. Let d= X -Y, where X and Y are random variables with normal distribution, and...
6. Let d= X -Y, where X and Y are random variables with normal distribution, and X and Y are independent random variables. Assume that you know both the mean and variance of   X and Y, if you have random samples from X and Y with equal sample size, what is the sampling distribution for the sample means of d(assuming X and Y are independent)?
Let X, Y be two random variables with a joint pmf f(x,y)=(x+y)/12 x=1,2 and y=1,2 zero...
Let X, Y be two random variables with a joint pmf f(x,y)=(x+y)/12 x=1,2 and y=1,2 zero elsewhere a)Are X and Y discrete or continuous random variables? b)Construct and joint probability distribution table by writing these probabilities in a rectangular array, recording each marginal pmf in the "margins" c)Determine if X and Y are Independent variables d)Find P(X>Y) e)Compute E(X), E(Y), E(X^2) and E(XY) f)Compute var(X) g) Compute cov(X,Y)
Let X ~ N(1,3) and Y~ N(5,7) be two independent random variables. Find... Var(X + Y...
Let X ~ N(1,3) and Y~ N(5,7) be two independent random variables. Find... Var(X + Y + 32) Var(X -Y) Var(2X - 4Y)
Let X and Y be two normal random variables. Given that the mean of X is...
Let X and Y be two normal random variables. Given that the mean of X is 6 and its standard deviation is equal to 1, and the mean of Y is 2 with standard deviation 3. What is the probability that Z= X-3Y is positive?.
X & Y are random variables Follow a joint probability distribution.    Have finite 1st & 2nd...
X & Y are random variables Follow a joint probability distribution.    Have finite 1st & 2nd moments. Var(X)≠0. Real numbers a & b, which minimize E[(Y – a − bX)^2] over all possible (a,b) are being determined for least squares/theoretical linear regression of Y on X. Solve f(a,b) = E[(Y – a − bX)^2] in order to find the critical points where the gradient equals 0. Differentiation & expectation can be switched with respect to a & b, such that...
Let U and V be two independent standard normal random variables, and let X = |U|...
Let U and V be two independent standard normal random variables, and let X = |U| and Y = |V|. Let R = Y/X and D = Y-X. (1) Find the joint density of (X,R) and that of (X,D). (2) Find the conditional density of X given R and of X given D. (3) Find the expectation of X given R and of X given D. (4) Find, in particular, the expectation of X given R = 1 and of...
Independent random variables X and Y follow binomial distributions with parameters(n1,θ) and (n2,θ). Let Z =X+Y....
Independent random variables X and Y follow binomial distributions with parameters(n1,θ) and (n2,θ). Let Z =X+Y. What will be the distribution of Z? Hint: Use moment generating function.
1) Suppose that X and Y are two random variables, which may be dependent and Var(X)=Var(Y)....
1) Suppose that X and Y are two random variables, which may be dependent and Var(X)=Var(Y). Assume that 0<Var(X+Y)<∞ and 0<Var(X-Y)<∞. Which of the following statements are NOT true? (There may be more than one correct answer) a. E(XY) = E(X)E(Y) b. E(X/Y) = E(X)/E(Y) c. (X+Y) and (X-Y) are correlated d. (X+Y) and (X-Y) are not correlated. 2) S.D(X ± Y) is equal to, where S.D means standard deviation a. S.D(X) ± S.D(Y) b. Var(X) ± Var(Y) c. Square...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT