Let the Random Variable X Represent the Winnings at One

question 54

Essay

Let the random variable X represent the winnings at one play of a particular game. The expected value of X is known to be -$0.32. Suppose a player plays the game five times and calculates his average winnings. Will the average definitely be equal to -$0.32? Now suppose the player plays the game 100 times and calculates his average winnings. Will the average definitely be equal to -$0.32? Which average is likely to be closer to -$0.32? Explain your answer with reference to the law of large numbers.

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Definitions:

Dramatic Effect

The significant impact or emotional response that an event, action, or scene in art and literature is intended to evoke.

Criminal Behavior

Activities that violate legal statutes and are subject to sanctions from the criminal justice system.

Education

The process of facilitating learning, or the acquisition of knowledge, skills, values, beliefs, and habits through various means such as teaching, training, storytelling, and research.

Incarceration Rates

The number of individuals confined in a prison or jail per 100,000 population.