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Fundamentals of Probability, with Stochastic Processes | 3rd Edition | ISBN: 9780131453401 | Authors: Saeed Ghahramani
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What are the expected value and variance of the number of

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QUESTION:

What are the expected value and variance of the number of full house hands in n poker hands? (See Exercise 20 of Section 2.4 for a definition of a full house.)

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QUESTION:

What are the expected value and variance of the number of full house hands in n poker hands? (See Exercise 20 of Section 2.4 for a definition of a full house.)

ANSWER:

Step 1 of 3

We include the definition of full house for the sake of convenience.

F'ull house: Three cards of one denomination and two cards of a second denomination: for example, three  's and two queens.

Thus to form a full house, choose one denomination out of 13 , and choose which three suits to be had for that denomination, which occurs in  ways. Next, choose the second denomination out of 12 remaining, and the three suits in again,  ways.

Thus the total number of ways

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