Let A be a random variable with probability density function f (x), and let M(t) = E[ ] be its…

Let A be a random variable with probability density function f(x), and let M(t) = E[] be its moment generating function The tilted density function f, is defined by

Let A, have density function ,

(a) Show that for any function h(x)

 

(b) Show that, for t > 0,

 

(c) Show that if P{X7 > a} = 1/2 then