A power plant supplies electric power for five cities 1-5 via high voltage power lines A-E, as shown in attachment. Suppose that a 7.0 earthquake will damage each high voltage power line independently with probability 0.2. A city has electric power only if all the high voltage power lines between the city and the power plant are intact. Let X denote the number of cities that lose electric power when a 7.0 earthquake hits. For instance, if power line C is the only one damaged, then X = 1 (city 3 loses power); if power line B is the only one damaged, then X = 2 (both cities 2 and 3 lose power). (a) Find P{X = 0} and P{X = 5}. (b) When a 7.0 earthquake hits, what is the probability that city 3 loses electric power, and what is the probability that city 5 loses electric power? (c) Compute E[X].
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.
A power plant supplies electric power for five cities 1-5 via high voltage power lines A-E, as shown in attachment.
Suppose that a 7.0 earthquake will damage each high voltage power line
independently with
Let X denote the number of cities that lose electric power when a 7.0 earthquake hits. For instance, if power line C is the only one damaged, then X = 1 (city 3 loses power); if power line B is the only one damaged, then X = 2 (both cities 2 and 3 lose power).
(a) Find P{X = 0} and P{X = 5}.
(b) When a 7.0 earthquake hits, what is the probability that city 3 loses electric power, and what is the probability that city 5 loses electric power?
(c) Compute E[X].
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