In the game of roulette, a player can place a $5 bet on the number 34 and have a 1/38 probability of winning. If the metal ball lands on 34, the player gets to keep the $5 paid to play the game and the player is awared an additional $175. Otherwise, the player is awarded nothing and the casino takes the player's $5. Find the average expected E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose. What is the expected value?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
In the game of roulette, a player can place a $5 bet on the number 34 and have a 1/38 probability of winning. If the metal ball lands on 34, the player gets to keep the $5 paid to play the game and the player is awared an additional $175. Otherwise, the player is awarded nothing and the casino takes the player's $5. Find the average expected E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose.
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