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" proposes a Poisson distribution for \( X \). Suppose that \( \mu = 4 \). (Round your answers to three decimal places.)(a) Compute both \( P(X \leq 4) \) and \( P(X < 4) \).\[ P(X \leq 4) = \, \_\_\_\_\_ \]\[ P(X < 4) = \, \_\_\_\_\_ \](b) Compute \( P(4 \leq X \leq 6) \).\[ \_\_\_\_\_ \](c) Compute \( P(6 \leq X) \).\[ \_\_\_\_\_ \](d) What is the probability that the number of anomalies does not exceed the mean value by more than one standard deviation?\[ \_\_\_\_\_ \]

Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3…

Answered: Let X be the number of material…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let X₁,..., Xn be a random sample from a distribution with one of two pdfs. If 0 = 1, then f(x;0=1) = 1 (0 < x < 1). If 0 = 2, then f(x;0= 2) = 2x1 (0 < x < 1). (a) Give a general form of the MLE of 0. (b) You are given a sample data of 3 values: 0.4, 0.5, 0.8. Find the MLE estimate of 0 based on the data.
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