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.
Can someone please explain it to me ASAP??!!!
(i) and (ii) please, thank you
Question 3. Let X₁,, Xn be a random sample from a distribution with the pdf given by f₁₁x(x) = exp(-ª) if x ≥ A, otherwise f(x) = 0, where > 0. Find the MLE's of 0 and X. Start by writing the likelihood function and note the constraint involving A. Question 4. #4.2.9 of the textbook.
Q 4.4. An individual picked at random from a population has a propensity to have accidents that is modelled by a random variable Y having the gamma distribution with shape parameter a and rate parameter ß. Given Y = y, the number of accidents that the individual suffers in years 1, 2, ..., n are independent random variables X₁, X2,... Xn each having the Poisson distribution with parameter y. (a) Write down a function f so that the joint distribution of Y, X₁, Xn can be described via P(a ≤ Y ≤ b, X₁ = k1, X₂ = k2 … . . Xn = kn) = [° ƒ (y, k1, k2, ... kn)dy and derive from this expression that, for your choice of f, Y has the Gamma distribution, and that conditionally on Y = y, X₁, X2,... Xn are independent, each having the Poisson distribution with parameter y.
Please do question 2e and 2f with full handwritten working out
An ion channel can be in either open (O) or closed (C) states. If it is open, then it has probability 0.1 of closing in 1 microsecond; if closed, it has probability 0.3 of opening in 1 microsecond.
Suppose that insurance companies did a survey. They randomly surveyed 450 drivers and found that 300 claimed to always buckle up. We are interested in the population proportion of drivers who claim to always buckle up. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a) (i) x = (ii) n = (ii) p'= (rounded to four decimal places) O Part (b) A Part (c) Which distribution should you use for this problem? (Round your answer to four decimal places.) P'- Explain your choice. O The normal distribution should be used because we are interested in proportions and the sample size is large. O The Student's t-distribution should be used because we do not know the standard deviation. O The Student's t-distribution should be used because Vnpg s 10, which implies a small sample. O The binomial distribution should be used because there are two outcomes, buckle up…

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