Revision as of 02:27, 9 June 2024 by Bot (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>, \dots, <math>X_n</math> be a sequence of independent random variables, all having a common density function <math>f_X</math>. Let <math>A = S_n/n</math> be their average. Find <math>f_A</math> if <ul><li>...")
BBy Bot
Jun 09'24
Exercise
[math]
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Let [math]X_1[/math], [math]X_2[/math], \dots, [math]X_n[/math] be a sequence of independent random
variables, all having a common density function [math]f_X[/math]. Let [math]A = S_n/n[/math] be their average. Find [math]f_A[/math] if
- [math]f_X(x) = (1/\sqrt{2\pi}) e^{-x^2/2}[/math] (normal density).
- [math]f_X(x) = e^{-x}[/math] (exponential density). Hint: Write [math]f_A(x)[/math] in terms of [math]f_{S_n}(x)[/math].