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# Thread: may 2005 exam question

1. ## may 2005 exam question

Hello. I have a question from the may 2005 exam

the question was: Find the expected number of rolls of a die in order to get the first three sixes.

Thank you

2. I think the question asked for the VARIANCE, not the expectation

"Find the variance of the number of rolls of a die in order to get three sixes"

Anyway, I used the formula of the NEGATIVE BINOMIAL. Is that right?

3. ## Negative binomial

Yes. Did it say clearly whether you count the last roll or not? Or whether the rolls that result in a six are counted?

Yours,
Krzys'

Originally Posted by nerdjyack
I think the question asked for the VARIANCE, not the expectation

"Find the variance of the number of rolls of a die in order to get three sixes"

Anyway, I used the formula of the NEGATIVE BINOMIAL. Is that right?

4. The question was finding the variance of the Total number of rolls.

Total Number of Rolls = X number of failures + 3 successes.
So Var (Total) = Var(X) = 90, by the formula for negative binomial, with r = 3, p = 1/6.

5. I can't remember exactly what the question asked, I just remember that it said to approximate it with the normal distribution. I think there were three parts to this question:

1. Recognize that the presented scenario was a negative binomial.
2. Recall the variance and mean formulas and use them to figure out what the variance and mean for that distribution was.
3. Use that mean and variance and a normal approximation to calculate what you were being asked (I don't remember what they asked for but I remember the answer I got was one of the choices =/ )

6. I don't recall the question asking to approximate it using the normal distribution. I believe that was a different question.

Anyway, 90 was also my answer. I hope it's right!

7. I wasn't really sure how to do it, but I believe I guessed 90, so I hope you're right too.