Question: 1.2.1 Thirteen cards numbered 1; : : : ;13 are shuffled and dealt one at a time. Say a match occurs on deal k if

1.2.1 Thirteen cards numbered 1; : : : ;13 are shuffled and dealt one at a time. Say a match occurs on deal k if the kth card revealed is card number k. Let N be the total number of matches that occur in the thirteen cards. Determine E[N].

Hint: Write N D 1fA1gC C1fA13g where Ak is the event that a match occurs on deal k.

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