exercise:15f9b201c6: 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> Let <math>S_n</math> be the number of successes in <math>n</math> Bernoulli trials with probability .8 for success on each trial. Let <math>A_n = S_n/n</math> be the average number of successes. In each case give the value for the limit, and gi...")
 
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<div class="d-none"><math>
Let <math>S_n</math> be the number of successes in <math>n</math> Bernoulli trials with probability .8 for success on each trial.  Let <math>A_n = S_n/n</math> be the average number of successes.  
\newcommand{\NA}{{\rm NA}}
\newcommand{\mat}[1]{{\bf#1}}
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\newcommand{\mathds}{\mathbb}</math></div>  Let <math>S_n</math> be the number of successes in <math>n</math> Bernoulli trials with
probability .8 for success on each trial.  Let <math>A_n = S_n/n</math> be the average number of successes.  
In each case give the value for the limit, and give a reason for your answer.
In each case give the value for the limit, and give a reason for your answer.
<ul><li>  <math>\lim_{n \to \infty} P(A_n = .8)</math>.
<ul style="list-style-type:lower-alpha"><li>  <math>\lim_{n \to \infty} P(A_n = .8)</math>.
</li>
</li>
<li>  <math>\lim_{n \to \infty} P(.7n  <  S_n  <  .9n)</math>.
<li>  <math>\lim_{n \to \infty} P(.7n  <  S_n  <  .9n)</math>.

Latest revision as of 22:58, 14 June 2024

Let [math]S_n[/math] be the number of successes in [math]n[/math] Bernoulli trials with probability .8 for success on each trial. Let [math]A_n = S_n/n[/math] be the average number of successes. In each case give the value for the limit, and give a reason for your answer.

  • [math]\lim_{n \to \infty} P(A_n = .8)[/math].
  • [math]\lim_{n \to \infty} P(.7n \lt S_n \lt .9n)[/math].
  • [math]\lim_{n \to \infty} P(S_n \lt .8n + .8\sqrt n)[/math].
  • [math]\lim_{n \to \infty} P(.79 \lt A_n \lt .81)[/math].