Suppose two players A and B are trying to throw a basketball through a loop. The

Q: Suppose two players A and B are trying to throw a basketball through a loop. The

a) Player A: Ya = Xa + r E( Ya ) = E( Xa ) + r --> E( Ya ) = ( r/p - r ) + r = r/p Player B: Yb = Xb + mr E( Yb ) = E( Xb ) + mr --> E( Yb ) = ( mr/mp - mr ) + mr = r/p Therefore expected number of throws is the same. b) b) Variance of Player B is smaller

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Suppose two players A and B are trying to throw a basketball through a loop. The probability
that player A will succeed on any given throw is p, and he throws until he has succeed r times. See screenshot for full question.

19. Suppose two players A and B are trying to throw a basketball through a loop. The probability that player A will succeed on any given throw is p, and he throws until he has succeed r times. The probability that player B will succeed on any given throw is mp, where m is a given integer (m = 2, 3, ...) such that mp

Explanation / Answer

Player A: Ya = Xa + r
E( Ya ) = E( Xa ) + r --> E( Ya ) = ( r/p - r ) + r = r/p

Player B: Yb = Xb + mr
E( Yb ) = E( Xb ) + mr --> E( Yb ) = ( mr/mp - mr ) + mr = r/p

Therefore expected number of throws is the same.

b) b) Variance of Player B is smaller

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Suppose two players A and B are trying to throw a basketball through a loop. The

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