ame 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) Let X be the number of times it takes for you to get your first win. What distribution does X follow, and what are the expection and variance of X? (b) If you play until you win once, what is your expected net profit (positive for profit, negative for loss)? What is the variance? (c) You start with $20. What is the probability that you lose all of your money without winning even once?
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 probability 0.15 on each round, but if you lose, you pay $2.
(a) Let X be the number of times it takes for you to get your first win. What distribution does X follow, and what are the expection and variance of X?
(b) If you play until you win once, what is your expected net profit (positive for profit, negative for loss)? What is the variance?
(c) You start with $20. What is the probability that you lose all of your money without winning even once?
X will follow geometric distribution with p = 0.15
The distribution of X will be:
The expectation and variance of X will be:
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