Let [math]X_1[/math], [math]X_2[/math], ..., [math]X_n[/math] be an independent trials process with density

[[math]] f(x) = \frac12 e^{-|x|}, \qquad -\infty \lt x \lt +\infty\ . [[/math]]

• Find the mean and variance of [math]f(x)[/math].
• Find the moment generating function for [math]X_1[/math], [math]S_n[/math], [math]A_n[/math], and [math]S_n^*[/math].
• What can you say about the moment generating function of [math]S_n^*[/math] as [math]n \to \infty[/math]?
• What can you say about the moment generating function of [math]A_n[/math] as [math]n \to \infty[/math]?