Revision as of 03:17, 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> (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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Jun 09'24
Exercise
[math]
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(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