Question

Let Θ ∼ Unif.([0, 2π]) and consider X = cos(Θ) and Y = sin(Θ). Can you...

Let Θ ∼ Unif.([0, 2π]) and consider X = cos(Θ) and Y = sin(Θ).

Can you find E[X], E[Y], and E[XY]?

clearly, x and y are not independent

I think E[X] = E[Y] = 0 but how do you find E[XY]?

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

Homework Answers

Answer #2

similarly E(Y) = 0

XY = sin *cos

period of sin = 2 pi , sin 2 = pi , hence integral is 0

Please rate

answered by: anonymous
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
Identify the surface with parametrization x = 3 cos θ sin φ, y = 3 sin...
Identify the surface with parametrization x = 3 cos θ sin φ, y = 3 sin θ sin φ, z = cos φ where 0 ≤ θ ≤ 2π and 0 ≤ φ ≤ π. Hint: Find an equation of the form F(x, y, z) = 0 for this surface by eliminating θ and φ from the equations above. (b) Calculate a parametrization for the tangent plane to the surface at (θ, φ) = (π/3, π/4).
3. Let P = (a cos θ, b sin θ), where θ is not a multiple...
3. Let P = (a cos θ, b sin θ), where θ is not a multiple of π/2 be a point on the ellipse (x 2/ a2 )+ (y 2/ b 2) = 1, where a ≥ b > 0; and let P1 = (a cos θ, a sin θ) the corresponding on the circle x 2 /a2 + y 2/ a2 = 1. Prove that the tangent to the ellipse at P and the tangent to the circle at...
Find the dimension of the subspace U = span {1,sin^2(θ), cos 2θ} of F[0, 2π]
Find the dimension of the subspace U = span {1,sin^2(θ), cos 2θ} of F[0, 2π]
Consider the function on the interval (0, 2π). f(x) = sin(x)/ 2 + (cos(x))2 (a) Find...
Consider the function on the interval (0, 2π). f(x) = sin(x)/ 2 + (cos(x))2 (a) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing     decreasing     (b) Apply the First Derivative Test to identify the relative extrema. relative maximum     (x, y) =    relative minimum (x, y) =
With the parametric equation x=cos(t)+tsin(t), y=sin(t)-tcos(t) , 0 ≤ t ≤ 2π) Find the length of...
With the parametric equation x=cos(t)+tsin(t), y=sin(t)-tcos(t) , 0 ≤ t ≤ 2π) Find the length of the given curve. (10 point)     2) In the circle of r = 6, the area above the r = 3 cos (θ) line Write the integral or integrals expressing the area of ​​this region by drawing. (10 point)
Consider the function on the interval (0, 2π). f(x) = sin(x) cos(x) + 4. (A) Find...
Consider the function on the interval (0, 2π). f(x) = sin(x) cos(x) + 4. (A) Find the open interval(s) on which the function is increasing or decreasing. (Enter your answers using interval notation.) (B) Apply the First Derivative Test to identify all relative extrema.
Let f(x)=sin x-cos x,0≤x≤2π Find all inflation point(s) of f. Find all interval(s) on which f...
Let f(x)=sin x-cos x,0≤x≤2π Find all inflation point(s) of f. Find all interval(s) on which f is concave downward.
Consider the function on the interval (0, 2π). f(x) = sin(x) cos(x) + 2 (a) Find...
Consider the function on the interval (0, 2π). f(x) = sin(x) cos(x) + 2 (a) Find the open interval(s) on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing Incorrect: Your answer is incorrect. decreasing Incorrect: Your answer is incorrect. (b) Apply the First Derivative Test to identify all relative extrema. relative maxima (x, y) = Incorrect: Your answer is incorrect. (smaller x-value) (x, y) = Incorrect: Your answer is incorrect. (larger x-value) relative minima...
Let X i ~ Unif(0, 1) for 1 <= i <= n be IID (independent identically...
Let X i ~ Unif(0, 1) for 1 <= i <= n be IID (independent identically distributed) random variables. Let Y = max(X 1 , …, X n ). What is E(Y)?
Let X = (X1, X2) T be a two-dim random vector, and (R, Θ) be its...
Let X = (X1, X2) T be a two-dim random vector, and (R, Θ) be its polar coordinates, i.e. X1 = R cos(Θ) and X2 = R sin(Θ). Show that X is spherically symmetric if and only if R and Θ are independent, and Θ ∼Uniform(0, 2π).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT