A random variable has outcomes Success and Failure with probabilities and respectively. A gambler observes the sequence of outcomes of this variable and receives a prize of if is the first time that Success occurs. What is the expected value of the gambler's prize?
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A random variable has outcomes Success and Failure with probabilities 3/4 and 1/4 respectively. A gambler observes the sequence of outcomes of this variable and receives a prize of 2ⁿ if n is the first time that Success occurs. What is the expected value of the gambler's prize? (A) 1 (B) 2 (C) 3 (D) 4
Also written as: A random variable has outcomes Success and Failure with probabilities 3/4 and 1/4 respectively. A gambler observes the sequence of outcomes of this variable and receives a prize of 2^n if n is the first time that Success occurs. What is the expected value of the gambler's prize?
Random variables and standard distributions has come up 173 times in 7 exams since 2005.
This question is on Geometric and hypergeometric distributions, part of Random variables and standard distributions in Statistics.
Waiting for a first success, and successes in draws without replacement.
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Question from the DSE 2005 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.