Homework 7 (Optional) Answers

BSTA 550

Questions

Extra problems

4. (a) Poisson\((\sum_{i=1}^n \lambda_i)\)     (b) Poisson\((3\lambda)\)      (c) \(M_{3X}(t)=e{\lambda(e^{3t}-1)}\) This is not an mgf of a common probability distribution.

4. In (b) we are adding independent r.v.’s \(X_i\), while in (c) we are adding dependent r.v.’s (\(3X=X+X+X\); \(X\) is dependent with itself).