This problem demonstrates the concept of redundancy, the principle of improving reliability of systems by using redundant or backup components. Suppose a hydraulic system on an airplane has a 5% probability of failing. a) What is the probability that the hydraulic system does not fail (that is, the flight is completed safely)? b) Now, suppose that the airplane has three independent hydraulic systems that each have a 5% probability of failure. What is the probability that all three systems fail? c) Supposing that the airplane will safely complete its flight if at least one of the three independent hydraulic systems is functioning, what is the probability that the airplane will safely complete its flight? d) What effect does having a redundancy of three independent hydraulic systems have on the probability of a safe flight?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
This problem demonstrates the concept of redundancy, the principle of improving reliability of systems by using redundant or backup components. Suppose a hydraulic system on an airplane has a 5%
a) What is the probability that the hydraulic system does not fail (that is, the flight is completed safely)?
b) Now, suppose that the airplane has three independent hydraulic systems that each have a 5% probability of failure. What is the probability that all three systems fail?
c) Supposing that the airplane will safely complete its flight if at least one of the three independent hydraulic systems is
d) What effect does having a redundancy of three independent hydraulic systems have on the probability of a safe flight?
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