marmbite
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A random number generator on a computer is used to produce integers from 1 to 5 inclusive. Ahmed writes a program which will produce a sequence of these integers which ends when 5 has been obtained. The number, n, of integers in the sequence is counted and stored. The procedure is repeated 1000 times and Σn obtained. On a particular run of this program the value of Σn was 5096. Estimate the probability of the computer generating a 5.

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Gregorius
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(Original post by marmbite)
A random number generator on a computer is used to produce integers from 1 to 5 inclusive. Ahmed writes a program which will produce a sequence of these integers which ends when 5 has been obtained. The number, n, of integers in the sequence is counted and stored. The procedure is repeated 1000 times and Σn obtained. On a particular run of this program the value of Σn was 5096. Estimate the probability of the computer generating a 5.

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You are looking at a sequence of Bernoulli trials where the events are "five generated" and "not a five generated" and are concerned with the the number of trials until the event "five generated" occurs.

So, have you ever heard of the "geometric distribution"? The question is asking you to estimate the parameter of this distribution from the observed data.

If you have never heard of the geometric distribution, the question is then asking you to work it out from first principles!

So, if the probability of generating a five is p (and therefore that the probability of generating something other than a five is (1-p)), what is the probability of having to generate k numbers before a five appears?
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marmbite
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(Original post by Gregorius)
You are looking at a sequence of Bernoulli trials where the events are "five generated" and "not a five generated" and are concerned with the the number of trials until the event "five generated" occurs.

So, have you ever heard of the "geometric distribution"? The question is asking you to estimate the parameter of this distribution from the observed data.

If you have never heard of the geometric distribution, the question is then asking you to work it out from first principles!

So, if the probability of generating a five is p (and therefore that the probability of generating something other than a five is (1-p)), what is the probability of having to generate k numbers before a five appears?
It's the final question in an exercise on geometric distribution. (Should have mentioned that in the original post)
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