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12.4 Exercise 6

Avg difficulty 2.5

(See Exercise 6 from "Problems on Mathematical Expectation"). A residential College plans to raise money by selling “chances” on a board. Fifty chances are sold. A player pays $10 to play; he or she wins $30 with probability p=0.2p = 0 . 2. The profit to the College is

X = 50 · 10 - 30 N , where N is the number of winners X = 50 \cdot 10 - 30 N , \text{where} N \text{is} \text{the} \text{number} \text{of} \text{winners}

Determine Var [X]Var \left[X\right].

Pfeiffer, Applied Probability, 12.4 Problems on Variance, Covariance, Linear Regression, exercise 6

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Adapted from Applied Probability © 2009 Paul E. Pfeiffer. Licensed under CC BY 3.0. Source: Applied Probability. Imported at revision d7a0420.