The number of red balls in an urn that contains n balls is a random variable that is equally…

The number of red balls in an urn that contains n balls is a random variable that is equally likely to be any of the values 0, 1, . .., n. That is, 1 P(i red, n – i non-red] = – i = 0, …, n n+lY The n balls are then randomly removed one at a time. Let Yk denote the number of red balls in the first k selections, k = 1, . . . , n. (a) Find P(Yn = j), j = 0, …, n. (b) Find P(Yn-, = j), j = 0, …, n. (c) What do you think is the value of P(Yk = j ), j = 0, . . . , n? (d) Verify your answer to part (c) by a backwards induction argument. That is, check that your answer is correct when k = n, and then show that whenever it is true for k it is also true for k – 1, k = 1, …, n.

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