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The joint probability density function of x and y is given by f(x,y)=(x+y)/8 0<x<2, 0<y<2 0...

The joint probability density function of x and y is given by f(x,y)=(x+y)/8 0<x<2, 0<y<2 0 otherwise

calculate the variance of (x+y)/2

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Answer #1

We first compute the first and second moments of (x + y)/2 here as:

Now the second moment of (x + y)/2 is obtained here as:

Now the variance of the given function here is obtained as:

Therefore 0.1389 is the required variance here.

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