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Hello, just a bit insecure about my answer.

Problem:-------

Suppose n people have throat cultures, and the cultures are then completely

mixed up. If we randomly pair off the n peoples’ names with the n cultures,

what is the expected number of correct labels?

---------------

So, here's my logic on the solution:

I think there are 2 random variables here, X1 for names, X2 for the cultures.

The formula for the expected value for 2 random variables is:

[tex]\sum_1^n \sum_1^n h(X1,X2)*prob(X1,X2)[/tex] for some weight function h.

I chose h(X1,X2) = 1. Also, I said prob(X1,X2) = (1/n^2). I hope all that is right so far. So just using the expected value equation, I simply said the answer is

[tex]\sum_1^n \sum_1^n (1)* \left \frac{1}{n^2} \right = 1[/tex]

Correct thinking? If not, what am I doing wrong?

Thanks in advance,

Mark

Problem:-------

Suppose n people have throat cultures, and the cultures are then completely

mixed up. If we randomly pair off the n peoples’ names with the n cultures,

what is the expected number of correct labels?

---------------

So, here's my logic on the solution:

I think there are 2 random variables here, X1 for names, X2 for the cultures.

The formula for the expected value for 2 random variables is:

[tex]\sum_1^n \sum_1^n h(X1,X2)*prob(X1,X2)[/tex] for some weight function h.

I chose h(X1,X2) = 1. Also, I said prob(X1,X2) = (1/n^2). I hope all that is right so far. So just using the expected value equation, I simply said the answer is

**1**.[tex]\sum_1^n \sum_1^n (1)* \left \frac{1}{n^2} \right = 1[/tex]

Correct thinking? If not, what am I doing wrong?

Thanks in advance,

Mark

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