Park et al. (1996) describe a method for generating correlated binary variables based on the follow scheme. Let X1,X2,X3 be independent Poisson random variables with mean λ1, λ2, λ3, respectively, and create the random variables
YI = X1 + X3 and Y2 = X2 + X3.
(a) Show that Cov(yi,y2) = λ3.
(b) Define Zi = I(Yt = 0) and p, = e~(λi'+ λ3) Show that Zi are Bernoulli(pi) with

(c) Show that the correlation of Z1 and Z2 is not unrestricted in the range [-1,1],

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P2Pi CorrZ1, Z2) S min