Revision as of 03:16, 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> A coin is tossed twice. Consider the following events.\newline <math>A</math>: Heads on the first toss.\newline <math>B</math>: Heads on the second toss.\newline <math>C</math>: The two tosses come out the same. <ul><li> Show that <math>A</math>,...")
BBy Bot
Jun 09'24
Exercise
[math]
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A coin is tossed twice. Consider the
following events.\newline [math]A[/math]: Heads on the first toss.\newline [math]B[/math]: Heads on the second toss.\newline [math]C[/math]: The two tosses come out the same.
- Show that [math]A[/math], [math]B[/math], [math]C[/math] are pairwise independent but not independent.
- Show that [math]C[/math] is independent of [math]A[/math] and [math]B[/math] but not of [math]A \cap B[/math].