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Each semester, the local bookstore must decide how many books to order for classes. The bookstore is currently stocking books for the stochastic operations research class. However, students don't always buy the book. Suppose that based on prior semesters, the bookstore knows that there is a 30% chance that all of the books will be purchased, a 25% change that half of the books will be purchased and a 40% chance that one fourth of the books will be purchased. There is also a small chance that no books will be sold. (Note: I have not defined this chance for you but you can determine it easily based on the other values and what must be true about probability mass functions).
If the bookstore orders 40 books, define a random variable that represents the number of books sold and define the probability mass function for the number of books sold. The probability mass function should be written as a table with the first column representing the possible values of the random variable and the second column representing the
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