Decide first if Binomial or Hypergeometric distributions is appropriate. Then write which one is most appropriate. Appeal to the formula given for this distribution to define p(x). Then calculate the Expected value and Variance for X.
We roll a fair, six- sided die twelve times.
(a) What is the total number of possible sequences of rolls?
(b) Where x is between 0 and 12, how many of those sequences of rolls have exactly x many "6"s? (Hint: Choose which x many of the twelve will be a "6" and multiply by the number of ways to fill out the rest of the sequence)
(c) Let X be the random variable measuring the number of "6"s rolled. Use the results from parts (a) and (b) to define the probability mass function, p(x), for X.