exercise:9700ad26c4: 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> 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>,...") |
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A coin is tossed twice. Consider the following events. | |||
<math>A</math>: Heads on the first toss. | |||
<math>B</math>: Heads on the second toss. | |||
following events. | |||
<math>A</math>: Heads on the first toss. | |||
<math>B</math>: Heads on the second toss. | |||
<math>C</math>: The two tosses come out the same. | <math>C</math>: The two tosses come out the same. | ||
<ul><li> Show that <math>A</math>, <math>B</math>, <math>C</math> are pairwise independent but not | |||
<ul style="list-style-type:lower-alpha"><li> Show that <math>A</math>, <math>B</math>, <math>C</math> are pairwise independent but not | |||
independent. | independent. | ||
</li> | </li> | ||
Latest revision as of 23:41, 12 June 2024
A coin is tossed twice. Consider the following events.
[math]A[/math]: Heads on the first toss.
[math]B[/math]: Heads on the second toss.
[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].