Question

a set of 1000 cards numbered 1 through 1000 is randomly distributed among 1000 peoplewith each receiving one card. compute the expected sum of the numbers on cards that are given topeople whose number matches the number on the card.

Answer 1

The probability shows that the expected number of cards given to people whose age matches the number on the card is 1.

How to compute the expected value?

From the information, a set of 1000 cards, numbered 1 through 1000, are distributed among 1000 people.

Let x be the random variable that's equal to the number of people who get a card.

Since we are looking for the expected value, this will be:

= E(X1 + X2 + .... X1000)

= 1