Question

Please answer both questions and I WILL rate if your answers are correct.

1.
(1 point) Given the MGF of random variable W is M(t)-e3.5e+14t provide the name of the distribution of W, as well as its parameters. Select all that apply. There may be more than one correct answer. A. normal(μ-14, σ2-3.5) B. gamma (a-3.5, β-14) C. normal(μ-3.5, σ2-14) E. gamma(α-14, β-7) F. normal(μ-14, σ2 . 7) G. gamma(α-14, β-3.5) H. gamma(α-7, β-14) I. None of the above

2.

Answer 1

1:

The given MGF can be written as:

$M(t)=e^{14t+\frac{1}{2}\cdot 7\cdot t^{2}}=e^{14t+\frac{1}{2}\cdot (\sqrt{7})^{2}\cdot t^{2}}$

It is MGF of normal distribution with parameters:

$\mu=14,\sigma^{2}=7,\sigma=\sqrt{7}$

Correct option is F.

2:

It is pdf of Gamma distribution with parameters as follows:

$\alpha=7,\beta=17$

Correct option is E.