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

The Correct Option is A

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