Question

If X and Y are normally distributed with the joint frequency function f(x,y)=e¹/⁶[2x-y²)+2xy/2π√3 , find the correlation coefficient between X and Y. Please proceed with any calculations, formulas, or explanations necessary to determine the correlation coefficient between X and (Y).

Answer 1

To find the correlation coefficient between X and Y, we need to calculate the covariance and the standard deviations of X and Y.

Step-by-step explanation:

To find the correlation coefficient between X and Y, we need to calculate the covariance and the standard deviations of X and Y.

The covariance, cov(X,Y), is calculated using the formula:

cov(X,Y) = E[(X - µX)(Y - µY)]

Where E denotes expectation, and µX and µY are the means of X and Y, respectively.

The standard deviations, σX and σY, are the square roots of the variances of X and Y, respectively.

The correlation coefficient, ρ, is then calculated as:

ρ = cov(X,Y) / (σX σY)

Given that X and Y have a joint frequency function f(x,y) = e^(1/6)[2x-y^2+2xy]/(2π√3), we can proceed to calculate the covariance and the standard deviations, and finally the correlation coefficient.