Bernoulli Trial help

**skyhawk714** · December 17th 2011, 06:00 AM

hey guys i have my final coming up and am really struggling. anyone care to help with this problem?

A probability experiment consists of conducting independent Bernoulli trials with probability of success 0.32 until the first success occurs. The expected number of failures preceding the first success has expected value

**chisigma** · December 17th 2011, 06:47 AM

Originally Posted by skyhawk714

hey guys i have my final coming up and am really struggling. anyone care to help with this problem?

A probability experiment consists of conducting independent Bernoulli trials with probability of success 0.32 until the first success occurs. The expected number of failures preceding the first success has expected value

Often it does happen that in [apparently...] difficult probability problems the solution is surprisingly simple!... in Bernoulli trials the probability to first succes at the n-th trial is...

$p_{n}=p\ (1-p)^{n-1}$ (1)

From (1) You derive that...

$E\{n\}= \sum_{n=1}^{\infty} n\ (1-p)^{n-1}\ p= p\ \sum_{n=1}^{\infty} n\ (1-p)^{n-1}$ (2)

Now You set $1-p=x$ and You obtain...

$E\{n\}= (1-x)\ \sum_{n=1}^{\infty} n\ x^{n-1} = (1-x)\ \frac{d}{d x} \frac{1}{1-x}= \frac{1}{1-x}=\frac{1}{p}$ (3)

Marry Christmas from Serbia

$\chi$ $\sigma$

Thread: Bernoulli Trial help

LinkBack

Thread Tools

Display

Bernoulli Trial help

Re: Bernoulli Trial help

Similar Math Help Forum Discussions

Trial and Error only ?

question and trial

Just a trial.

Bernoulli trial with conditional probability

Latex trial

Search Tags