In: Statistics and Probability
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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