Two service lines in a wastewater treatment plant that feed the secondary aeration basin. The proportions...

Two service lines in a wastewater treatment plant that feed the secondary aeration basin. The proportions of time that line 1 and line 2 are in use are given in term of the random variables of X and Y, respectively. The joint distribution describing the proportions X and Y of these two components is given by

f(x,y)={23(x2+y2),0≤x,y≤10,eleswhere

A. Determine if X and Y are independent.

B. The plant needs to have an idea of the combined proportions of the two lines in terms of

Z=X+Y

Find the following expected values:

E(X+Y)

E(XY)

C. Find Var(X), Var(Y), Cov(X,Y)

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