exercise:B2a45d5f2c: 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> Prove that, if <math>A_1</math>, <math>A_2</math>, \dots, <math>A_n</math> are independent events defined on a sample space <math>\Omega</math> and if <math>0 < P(A_j) < 1</math> for all <math>j</math>, then <math>\Omega</math> must have at le...") |
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Prove that, if <math>A_1</math>, <math>A_2</math>, \dots, <math>A_n</math> are independent events defined on a sample space <math>\Omega</math> and if <math>0 < P(A_j) < 1</math> for all <math>j</math>, then | |||
defined on a sample space <math>\Omega</math> and if <math>0 < P(A_j) < 1</math> for all <math>j</math>, then | |||
<math>\Omega</math> must have at least <math>2^n</math> points. | <math>\Omega</math> must have at least <math>2^n</math> points. | ||
Revision as of 00:12, 13 June 2024
Prove that, if [math]A_1[/math], [math]A_2[/math], \dots, [math]A_n[/math] are independent events defined on a sample space [math]\Omega[/math] and if [math]0 \lt P(A_j) \lt 1[/math] for all [math]j[/math], then [math]\Omega[/math] must have at least [math]2^n[/math] points.