Assume that X and Y are jointly continuous random variables with joint probability density function given by f(x,y)=beg∈{cases}136(3x−xy+4y) if 0&lt;x&lt;2 and 1&lt;y&lt;3∖0 othrewiseend{cases} Find Cov(X,Y).

Question

Assume that X and Y are jointly continuous random variables with joint probability density function given by  f(x,y)=beg∈{cases}136(3x−xy+4y) if 0&amp;lt;x&amp;lt;2 and 1&amp;lt;y&amp;lt;3∖0     othrewiseend{cases}  Find Cov(X,Y).

Viktor Wiley · Accepted Answer

Step 1  Covariance of two random variables X and Y with means E[X] and E[Y] is given below:  σXY=E(XY)−μXμY  =∑x∑yxyf(x,y)−{∑xxf(x,y)}×{∑yyf(x,y)}(∵For discrete)  =∫x∫vxyf(x,y)dydx−{∫xxg(x)dx}×{∫vyh(y)dy}(∵For cont∈uous)  The covariance of the random variable X and Y is obtained as shown below:  For E[XY],  E(XY)=∫x∫yxyf(x,y)dydx  =∫02∫13136xy(3x−xy+4y)dydx  =136∫02∫13(3x2y−x2y2+4xy2)dydx  =∫02(5x2+52x54)dx  =17681  Step 5  Therefore, the covariance of X and Y will be obtained as given below:  σXY=E(XY)−μXμY  =17681−(2827)(199)  =181(176−177.33)  =-0.01646

Assume that X and Y are jointly continuous random variables with joint probabili

Answered question

Answer & Explanation

New Questions in College Statistics