<t>For the first one, see that X Y and Z are vectors in a 3-d space (generated by X, Y,Z).The question can be re formulated as follows : knowing that the cosine between X and Y is 0.9, and the one between Y and Z is 0.8, we'd like to kniw the max and min cosines (X,Z).So X is on a cone surrounding Y...

The quickest way is to calculate , and then expand the exponential and identify the terms in equal powers of lambda.

A hint : the correlations you are talking about are the cosines of angles in the Hilbert space L²(Omega,P).