Ten balls are to be distributed among 5 urns, with each ball going into urn i with probabi...

Ten balls are to be distributed among 5 urns, with each ball going into urn i with probability

Let Xi denote the number of balls that go into urn i. Assume that events corresponding to the locations of different balls are independent.

(a) What type of random variable is Xi? Be as specific as possible.

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(b) For i ≠ j, what type of random variable is Xi + Xj?

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(c) Find P{X1 + X2 + X3 = 7}.