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.