ints is successful only with probability p. Consider the following game situation. The Temple Wildcats are losing by 14 points to the Killeen Tigers near the end of regulation time. The only way for Temple to win (or tie) this game is to score two touchdowns while not allowing Killeen to score again. The Temple coach must decide whet
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.
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Problem 4-05 (Algorithmic)
In American football, touchdowns are worth 6 points. After scoring a touchdown, the scoring team may subsequently attempt to score 1 or 2 additional points. Going for 1 point is virtually an assured success, while going for 2 points is successful only with
probability p. Consider the following game situation. The Temple Wildcats are losing by 14 points to the Killeen Tigers near the end of regulation time. The only way for Temple to win (or tie) this game is to score two touchdowns while not allowing Killeen to score again. The Temple coach must decide whether to attempt a 1-point or 2-point conversion after each touchdown. If the score is tied at the end of regulation time, the game goes into overtime. The Temple coach believes that there is a 43% chance that Temple will win if the game goes into overtime. The probability of successfully converting a 1-point conversion is 1.0. The probability of successfully converting a 2-point conversion is p.- Assume Temple will score two touchdowns and Killeen will not score. Create a decision tree for the decision of whether Temple's coach should go for a 1-point conversion or a 2-point conversion after each touchdown. The terminal nodes in the decision tree should be either WIN or LOSE for Temple.
Success (p) Go for 2 6 Win OT (43%) Success 3 Fail (1-p) 10 Lose OT (57%) Go for 2 2 Go for 1 Win OT (43%) Success (p) 11 Go for 2 7 Lose OT (57%) 4 Fail (1-p) 1 Go for 1 Success (p) Go for 2 8 Fail (1-p) 5 Win OT (43%) Go for 1 9 Lose OT (57%) - Assume that a WIN results in a value of 1.0 and LOSE results in a value of 0. Further, assume that the probability of converting a 2-point conversion is p = 36%. Should Temple's coach go for a 1-point conversion or 2-point conversion after scoring the first touchdown?
The Temple coach for 2 points after the first touchdown.
- Assume Temple will score two touchdowns and Killeen will not score. Create a decision tree for the decision of whether Temple's coach should go for a 1-point conversion or a 2-point conversion after each touchdown. The terminal nodes in the decision tree should be either WIN or LOSE for Temple.
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