Let X and Y be independent exponentially distributed random variables with parameter 1. Let Z=YX. (1) Compute the distribution function of (X, Z). (2) Are X and Z independent? (3) Compute E(Z|X=x).
a) (1) Not computable (2) Yes (3) e(−x)
b) (1) e(−x) (2) No (3) e(−x)
c) (1) Not computable (2) No (3) 1
d) (1) e(−x) (2) Yes (3) 1
