exercise:Ea4a38afb2: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> Let <math>X_1</math>, <math>X_2</math>, \ldots, <math>X_n</math> be an independent trials process with normal density of mean 1 and variance 2. Find the moment generating function for <ul><li> <math>X_1</math>. </li> <li> <math>S_2 = X_1 + X_2</m...") |
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Let <math>X_1</math>, <math>X_2</math>, \ldots, <math>X_n</math> be an independent trials process with | |||
normal density of mean 1 and variance 2. Find the moment generating function | normal density of mean 1 and variance 2. Find the moment generating function | ||
for | for | ||
<ul><li> <math>X_1</math>. | <ul style="list-style-type:lower-alpha"><li> <math>X_1</math>. | ||
</li> | </li> | ||
<li> <math>S_2 = X_1 + X_2</math>. | <li> <math>S_2 = X_1 + X_2</math>. | ||
Revision as of 00:06, 15 June 2024
Let [math]X_1[/math], [math]X_2[/math], \ldots, [math]X_n[/math] be an independent trials process with normal density of mean 1 and variance 2. Find the moment generating function for
- [math]X_1[/math].
- [math]S_2 = X_1 + X_2[/math].
- [math]S_n = X_1 + X_2 +\cdots+ X_n[/math].
- [math]A_n = S_n/n[/math].
- [math]S_n^* = (S_n - n\mu)/\sqrt{n\sigma^2}[/math].