Given: f(x,y) = 5 - 3x - y for 0 < x,y < 1 and x...

Given:

f(x,y) = 5 - 3x - y for 0 < x,y < 1 and x + y < 1, 0 otherwise

1) find the covariance of x and y

2) find the marginal probability density function for x

c) find the probability that x >= 0.6 given that y <= 0.2

Expert Solution

orchestra answered 2 years ago

Given f(x,y) = 2 ; 0< x ≤ y < 1 a. Prove that f(x,y) is...

Given f(x,y) = 2 ; 0< x ≤ y < 1 a. Prove that f(x,y) is a joint pdf. b. Find the correlation coefficient of X and Y.

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1 Let f(x, y) = 4xy, 0 < x < 1, 0 < y < 1,...

1 Let f(x, y) = 4xy, 0 < x < 1, 0 < y < 1, zero elsewhere, be the joint probability density function(pdf) of X and Y . Find P(0 < X < 1/2 , 1/4 < Y < 1) , P(X = Y ), and P(X < Y ). Notice that P(X = Y ) would be the volume under the surface f(x, y) = 4xy and above the line segment 0 < x = y < 1...

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