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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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. | |||
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 23:58, 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].