7. A gambler pays $10 to enter a game in which two coins are tossed. The gambler receives $25, $5 or nothing if two heads, one head or no heads appear, respectively. (a) Determine the expected return per game (ignore the $10 cost of playing). (b) The gambler decides to play until winning the $25 prize. Letting X denote the number of games played until two heads appear (the final game is the Xth game), find the probability function f(x) of X, show that its sum over all possible values of X is one, and find the expected value µ of X. (Note: this is not the expected return on this version of the game. Note too that X here is not quite the same as a geometric random variable, as it was defined in the lecture notes; however, thinking about such random variables will be helpful here).
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.
7. A gambler pays $10 to enter a game in which two coins are tossed. The gambler receives $25, $5 or nothing if two heads, one head or no heads appear, respectively.
(a) Determine the expected return per game (ignore the $10 cost of playing).
(b) The gambler decides to play until winning the $25 prize. Letting X denote the number of games played until two heads appear (the final game is the Xth game), find the
Step by step
Solved in 2 steps
