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Mathematical expectation The mathematical expectation of even terms.
Note that this problem is conditional distribution.

Values of Xi include odd and even numbers,

Therefore, the sum of probabilities that the sum of values is 2 4 6 8 10 must not be 1.

When listing distribution lists, the calculation method is as follows

For example, P(ξ=2)= P 1/P2

P 1 is an even number, 2 is 5/9, and the sum of these two numbers is the probability P2 of an even number.

So the sum of probabilities in the distribution list is 1.