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].

E[N] = 1

Step-by-step explanation:

Here is the hint we are given on this problem - " Write N = + + · · · + where is the event that a match occurs on deal k. "

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Now the standard thing is to do is let = 1, if there is a match on the -th pick and 0 otherwise. The number of matches is given to be + . . . + . Knowing that, we can use the linearity of expectation -

There are 13 cards and for -th pick, the probability of having a card with number is 1 / 13. Therefore, E[N] = E[ + . . . + ] = 1

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Solution: E[N] = 1

step-by-step explanation:

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column