A two dimensional variable (X, Y) is uniformly distributed over the square having the vertices (2,...

A two dimensional variable (X, Y) is uniformly distributed over the square having the vertices (2, 0), (0, 2), (-2, 0), and (0, -2).
(i) Find the joint probability density function.
(ii) Find associated marginal and conditional distributions.
(iii) Find E(X), E(Y), Var(X), Var(Y).
(iv) Find E(Y|X) and E(X|Y).
(v) Calculate coefficient of correlation between X and Y.

Expert Solution

ANSWER

------------------------------------

DEAR STUDENT,

IF YOU HAVE ANY QUERY ASK ME IN THE COMMENT BOX,I AM HERE TO HELPS YOU.PLEASE GIVE ME POSITIVE RATINGS

*****************THANK YOU***************

orchestra answered 2 years ago

Random variable X is uniformly distributed over the interval [2, b]. Given: P { |X –...

Random variable X is uniformly distributed over the interval [2, b]. Given: P { |X – 4 | > 4} = 0. 8. a) Find P { 0 < X < 5}

5. A continuous random variable X is uniformly distributed over (0,10). Compute the probability that an...

5. A continuous random variable X is uniformly distributed over (0,10). Compute the probability that an observed value of X will be within one standard deviation of its mean.

If X is uniformly distributed over (0, 1), find the fY (t) and E(Y ) of...

If X is uniformly distributed over (0, 1), find the fY (t) and E(Y ) of (a) Y = e X. (b)Y = − ln(X) (c) Y = cos(πX) (d)Y = sin(πX)

A point (a, b) is distributed uniformly in the square 0<x<1, 0<y<1. Let S(a, b) be...

A point (a, b) is distributed uniformly in the square 0<x<1, 0<y<1. Let S(a, b) be the area of a rectangle with sides a and b. Find P{1/4 < S(a, b) < 1/3}

Four protons are placed in the vertices of a square with a side of 2 x...

Four protons are placed in the vertices of a square with a side of 2 x 10^-9 m. A fifth proton is initially on the square perpendicular to its center, at a distance of 2 x 10^-9 m from it. Calculate (a) the minimum initial velocity that the fifth proton needs to reach the center of the square, (b) its initial and final accelerations. (c) Make a graph of the proton's potential energy as a function of its distance to...

Four protons are placed in the vertices of a square with a side of 2 x...

Four protons are placed in the vertices of a square with a side of 2 x 10-9 m. A fifth proton it is initially on the perpendicular to the square by its center, at a distance of 2 x 10-9 m from it. Calculate (a) the minimum initial velocity that the fifth proton needs to reach the center of the square, (b) its initial and final accelerations. (c) Make a graph of the proton's potential energy as a function of...

Question

A two dimensional variable (X, Y) is uniformly distributed over the square having the vertices (2,...

Solutions

Expert Solution

Related Solutions

Random variable X is uniformly distributed over the interval [2, b]. Given: P { |X –...

5. A continuous random variable X is uniformly distributed over (0,10). Compute the probability that an...

If X is uniformly distributed over (0, 1), find the fY (t) and E(Y ) of...

A point (a, b) is distributed uniformly in the square 0<x<1, 0<y<1. Let S(a, b) be...

Four protons are placed in the vertices of a square with a side of 2 x...

Four protons are placed in the vertices of a square with a side of 2 x...

A rectangle has one side on the x-axis and two vertices on the curve y=2/(1+x^2) Find...

Suppose we have a random variable X that is uniformly distributed between a = 0 and...

A random variable x is uniformly distributed between 20 and 52 . What is the expected...

Suppose (?,?) are distributed uniformly inside the quadrilateral ? with vertices (0,0), (2,0), (1,1), and (0,1)....