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    We have that a fair die is rolled until a 6 is obtained. Y is the number of rolls and X the number of 1s.

    We need the distribution of X given Y=k (k fixed greater or equal to 1)

    We then want the E(X) and Variance(X)

    So I'm thinking that X is simply (1/6)^(k-1), is that correct?
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    (Original post by pineapplechemist)
    We have that a fair die is rolled until a 6 is obtained. Y is the number of rolls and X the number of 1s.

    We need the distribution of X given Y=k (k fixed greater or equal to 1)

    We then want the E(X) and Variance(X)

    So I'm thinking that X is simply (1/6)^(k-1), is that correct?
    Well X is a random variable, not a number.

    If you meant that for E(X), then that's not correct.

    If a roll of 6 terminates the sequence of rolls, then all the rolls prior to that are not 6, i.e. they only have 5 choices each.

    Consider: What do you know about the k-1 initial rolls?

    Edit: And X is going to have a certain simple distribution.
 
 
 
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