exercise:968e1d0ecf: 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> (Johnsonbough<ref group="Notes" >R. Johnsonbough, “Problem \#103,” ''Two Year College Math Journal,'' vol. 8 (1977), p. 292.</ref>) A coin with probability <math>p</math> for heads is tossed <math>n</math> times. Let <math>E</math> be the ev...") |
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(Johnsonbough<ref group="Notes" >R. Johnsonbough, “Problem #103,” ''Two Year College Math Journal,'' vol. 8 (1977), p. 292.</ref>) A coin with probability <math>p</math> for heads is tossed <math>n</math> times. Let <math>E</math> be the event “a head is obtained on the | |||
<math>p</math> for heads is tossed <math>n</math> times. Let <math>E</math> be the event “a head is obtained on the | |||
first toss' and <math>F_k</math> the event `exactly <math>k</math> heads are obtained.” For which | first toss' and <math>F_k</math> the event `exactly <math>k</math> heads are obtained.” For which | ||
pairs <math>(n,k)</math> are <math>E</math> and <math>F_k</math> independent? | pairs <math>(n,k)</math> are <math>E</math> and <math>F_k</math> independent? | ||
Latest revision as of 00:47, 13 June 2024
(Johnsonbough[Notes 1]) A coin with probability [math]p[/math] for heads is tossed [math]n[/math] times. Let [math]E[/math] be the event “a head is obtained on the first toss' and [math]F_k[/math] the event `exactly [math]k[/math] heads are obtained.” For which pairs [math](n,k)[/math] are [math]E[/math] and [math]F_k[/math] independent?
Notes