Let X be the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. The article “Methodology for Probabilistic Life Prediction of Multiple-Anomaly Materials” (Amer. Inst. of Aeronautics and Astronautics J., 2006: 787–793) proposes a Poisson distribution for X. Suppose that μ = 4. a. Compute both P(X <= 4) and P(X < 4). b. Compute P(4 <= X <= 8). c. Compute P(8 <= 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.
Let X be the number of material anomalies occurring in
a particular region of an aircraft gas-turbine disk. The
article “Methodology for Probabilistic Life Prediction
of Multiple-Anomaly Materials” (Amer. Inst. of
Aeronautics and Astronautics J., 2006: 787–793) proposes a Poisson distribution for X. Suppose that μ = 4.
a. Compute both P(X <= 4) and P(X < 4).
b. Compute P(4 <= X <= 8).
c. Compute P(8 <= X).
d. What is the probability that the number of anomalies
exceeds its mean value by no more than one standard
deviation?
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