You are playing a game at a carnival. It costs nothing to play. You can win $5 with probability 0.15 on each round, but if you lose, you pay $2. (a) assume you have enough money to keep playing until you get bored, which happens after you play 20 rounds. Let Y be the number of times you win in 20 rounds. What is the distribution of Y ? (b) What is the expectation of the number of times you win in 20 rounds? What is the expectation of the amount of money that you have won (positive for net profit, negative for net loss), and what is the variance?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
You are playing a game at a carnival. It costs nothing to play. You can win $5 with
(a) assume you have enough money to keep playing until you get bored, which happens after you play 20 rounds. Let Y be the number of times you win in 20 rounds.
What is the distribution of Y ?
(b) What is the expectation of the number of times you win in 20 rounds?
What is the expectation of the amount of money that you have won (positive for net profit, negative for net loss), and what is the variance?
A binomial random variable X represents the number of successes among the total fix trials n. Here, the game is played for 20 fix rounds, thus total number of trials is 20. The probability of winning is 0.15 and this is equal for each trial. Each trial does not affect the outcome of other trial, so each trial is independent.
As the given case satisfies all the conditions of binomial distribution thus number of wins Y represents the binomial random variable with 20 trials and 0.15 probability of success in each trial.
The probability distribution for binomial distribution is given by . Substitute y for x, .
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