Question

If M(t), t ∈ $\R$, is the moment generating function of a random variable, then which one of the following is NOT the moment generating function of any random variable ?

• A. $\frac{5e^{-5t}}{1-4t^2}M(t),|t| < \frac{1}{2}$
• B. e-tM(t), t ∈ $\R$
• C. $\frac{1+e^t}{2(2-e^t)}M(t), t < \ln2$
• D. M(4t), t ∈ $\R$

Answer 1

Answer: (A)

$\frac{5e^{-5t}}{1-4t^2}M(t),|t| < \frac{1}{2}$

Answer 2

The correct option is (A) : $\frac{5e^{-5t}}{1-4t^2}M(t),|t| < \frac{1}{2}$.