Question
2.33 X and Y are independent zero mean Gaussian random variables with variances sigma^2 x, and...
2.33 X and Y are independent zero mean Gaussian random variables with variances sigma^2 x, and sigma^2 y. Let Z = 1/2(X + Y) and W =1/2 (X - Y) a. Find the joint pdf fz, w(z, w). b. Find the marginal pdf f(z). c. Are Z and W independent?
Homework Answers
Answer #1
Not the answer you're looking for?
Similar Questions
The random variables, X and Y , have the joint pmf f(x,y)=c(x+2y), x=1,2 y=1,2 and zero...
The random variables, X and Y , have the joint pmf
f(x,y)=c(x+2y), x=1,2 y=1,2 and zero otherwise.
1. Find the constant, c, such that f(x,y) is a valid pmf.
2. Find the marginal distributions for X and Y .
3. Find the marginal means for both random variables.
4. Find the marginal variances for both random variables.
5. Find the correlation of X and Y .
6. Are the two variables independent? Justify.
Suppose that X and Y are independent Uniform(0,1) random variables. And let U = X +...
Suppose that X and Y are independent Uniform(0,1) random
variables. And let U = X + Y and V = Y .
(a) Find the joint PDF of U and V
(b) Find the marginal PDF of U.
1. Let (X,Y ) be a pair of random variables with joint pdf given by f(x,y)...
1. Let (X,Y ) be a pair of random variables with joint pdf given
by f(x,y) = 1(0 < x < 1,0 < y < 1).
(a) Find P(X + Y ≤ 1).
(b) Find P(|X −Y|≤ 1/2).
(c) Find the joint cdf F(x,y) of (X,Y ) for all (x,y) ∈R×R.
(d) Find the marginal pdf fX of X. (e) Find the marginal pdf fY
of Y .
(f) Find the conditional pdf f(x|y) of X|Y = y for 0...
Assume X and. Y are. 2. independent variables that follow the standard uniform distribution i.e. U(0,1)...
Assume X and. Y are. 2. independent variables that follow the
standard uniform distribution i.e. U(0,1)
Let Z = X + Y
Find the PDF of Z, fZ(z) by first obtaining the CDF
FZ(z) using the following steps:
(a) Draw an x-y axis plot, and sketch on this plot the lines
z=0.5, z=1, and z=1.5 (remembering z=x+y)
(b) Use this plot to obtain the function which describes the
area below the lines for z = x + y in terms...
STAT 180 Let X and Y be independent exponential random variables with mean equals to 4....
STAT 180 Let X and Y be independent exponential random variables
with mean equals to 4.
1) What is the covariance between XY and X.
2) Let Z = max ( X, Y). Find the Probability Density Function
(PDF) of Z.
3) Use the answer in part 2 to compute the E(Z).
Let X and Y be random variables with the joint pdf fX,Y(x,y) = 6x, 0 ≤...
Let X and Y be random variables with the joint pdf
fX,Y(x,y) = 6x, 0 ≤ y ≤ 1−x, 0 ≤ x ≤1.
1. Are X and Y independent? Explain with a picture.
2. Find the marginal pdf fX(x).
3. Find P( Y < 1/8 | X = 1/2 )
Suppose X and Y are continuous random variables with joint pdf f(x,y) = x + y,...
Suppose X and Y are continuous random variables with joint
pdf
f(x,y) = x + y, 0 < x< 1, 0 < y< 1. Let W =
max(X,Y). Find EW.
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 and Y be independent random variables, with X following uniform distribution in the interval...
Let X and Y be independent random variables, with X following
uniform distribution in the interval (0, 1) and Y has an Exp (1)
distribution.
a) Determine the joint distribution of Z = X + Y and Y.
b) Determine the marginal distribution of Z.
c) Can we say that Z and Y are independent? Good
Suppose X and Y are continuous random variables with joint pdf f(x,y) = 2(x+y) if 0...
Suppose X and Y are continuous random variables with joint pdf
f(x,y) = 2(x+y) if 0 < x < < y < 1 and 0 otherwise.
Find the marginal pdf of T if S=X and T = XY. Use the joint pdf of
S = X and T = XY.
ADVERTISEMENT
Need Online Homework Help?
Get Answers For Free
Most questions answered within 1 hours.
ADVERTISEMENT
Active Questions
asked 5 minutes ago
asked 14 minutes ago
asked 20 minutes ago
asked 33 minutes ago
asked 34 minutes ago
asked 36 minutes ago
asked 48 minutes ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago