Moment generating functions, Task 2. Suppose that the continuous random variable, X, has a probability density function of the following form, for parameter 1> 0: A x exp (–Xr), T> 0, [0. fx(x): otherwise. (a) Show that X has moment-generating function: +3 M(t) : t< A.

Moment generating functions, Task 2. Suppose that the continuous random variable, X, has a probability density function of the following form, for parameter 1> 0: A x exp (–Xr), T> 0, [0. fx(x): otherwise. (a) Show that X has moment-generating function: +3 M(t) : t< A.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Moment generating functions, Task 2.
Suppose that the continuous random variable, X, has a probability density
function of the following form, for parameter X> 0:
322
SA x exp (–Xx), x> 0,
10.
2
fx(x) =
otherwise.
(a) Show that X has moment-generating function:
M(t) = ( 1
t< A.
II

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