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I'm working on an assignment and I'm more or less new to stats. It might be the wording of the questions that's getting me as well. It deals with a regular 6-sided die.

1.a) What is the mean number of throws between the appearances of a six?

So I think this means if you have already rolled a 6, how many rolls until you get another.

$n=\frac{1}{p}=6$ rolls

b) At any stage of the process, what is the mean number of throws before the next appearance of a six?

Since each roll is independent of the previous one, the mean number of rolls is just:

$n=\frac{1}{p}=6$

c) At any stage of the process, what is the mean number of throws since the last appearance of a six?

Why would the process be any different forward or in reverse?

$n=\frac{1}{p}=6$

Am I reading these wrong? I get the same answer for all parts and that doesn't seem right.

Bobson Dugnutt
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BobJoe1803
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1 Answers1

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All your answers are right. Perhaps the reason they don't seem right to you is that one might expect the answer to a) to be the sum of the answers to b) and c). That's not the case, however. The question whose answer is the sum of the answers to b) and c) is: At any stage of the process, what is the mean number of rolls from the last appearance of a six to the next appearance of a six? By contrast, a) doesn't ask about a given stage of the process. It counts every stretch between two sixes with the same weight, whereas if you ask about a given stage of the process, you're giving more weight to longer stretches, since your given stage of the process is more likely to be in a longer stretch than in a shorter stretch.

joriki
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