Question: Dear tutors, if you do not know how to do the question, please do not send it for revision because there is NOTHING wrong with

Dear tutors, if you do not know how to do the question, please do not send it for revision because there is NOTHING wrong with the question. J

ust leave it there for other tutors to solve. Thank you

Suppose you are throwing n balls into two bins, labeled A and B. Each ball goes into bin A with probability 1/2 and bin B with probability 1/2, and the balls are thrown independently. Let NA be the total number of balls in bin A after all n balls have been thrown. (a) Let X, be the indicator random variable that equals 1 when the i'th ball falls in bin A and equals 0 otherwise. What is E[X;]? What is E[X ]? What is E[X, Xy] for i # j? (b) Compute E[NA] and E[ N ]. Hint: Write NA in terms of the indicator random variables X1, . . . ; Xn

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