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7.39 Suppose that 2 balls are randomly removed from an urn containing n red and m blue balls. Let X = 1 if the ith ball removed is red, and let it be 0 otherwise, i = 1,2.a. Do you think that Cov(X1, X2) is negative, zero, or positive.b. Validate your answer to part (a).Suppose the red balls are numbered, and let Y; equal 1 if redball number i is removed, and let it be 0 if that ball is notremoved.c. Do you think that Cov(Y, Y₂) is negative, zero, or positive.d. Validate your answer to part (c).

Sagot :

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(a)let A=event that first k-1 draws will get r-1 red balls

let B=event that last (kth) draw will get rth red ball

P(kth draw is the rth red ball)= P(A AND B) = P(A)xP(B)

(b)P(A)=  # of  ways to draw r-1 red balls in k-1 trail

         # of ways to draw k-1 balls

RBBB *R is one way to achieve P(A AND B)

BBBR *R is another way.

(c)There are n−(r−1) red left, and a total of (m+n)−(k−1) balls left, so the (conditional) probability of drawing a red on the kth trial is n−r+1/m+n−k+1 Thus our required probability is

So,  P(A)= nC(r-1) x mC(n-r) x 1/(n+m)C(k-1)

Know more about probability at:

brainly.com/question/24756209

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