Joe plays Blackjack at a casino table, and wins each game with probability p, independent of outcomes of previous games. In the first n games, let W denote the number of wins, and L the number of losses. Assume that n ≥ 2. Given that Joe won the first two games, compute the conditional expectation and the conditional variance of the random variable W.
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.
Joe plays Blackjack at a casino table, and wins each game with probability p, independent of outcomes of previous games. In the first n games, let W denote the number of wins, and L the number of losses.
Assume that n ≥ 2. Given that Joe won the first two games, compute the conditional expectation and the conditional variance of the random variable W.
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