The Pareto distribution with parameter a has range [1, ∞) and pdff(x)=αxaSuppose the data5, 2, 3was drawn independently from such a distribution. Find the maximum likelihood estimate(MLE) of a.

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Answered: Suppose the data f(x) = α xa 5, 2, 3…

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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The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table below. At a=0.10, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 10.4 8.2 8.8 12.6 13.1 6.1 9.90 11.3 (a) Write the claim mathematically and identify Ho and Ha Which of the following correctly states Ho and H₂? Ο Α. Ho: με 11.0 H₂>11.0 O D. Ho: 11.0 H: ≤11.0 A O A. Fail to reject Ho because the P-value is greater than the significance level. OB. Reject H, because the P-value is greater than the significance level. OC. Reject Ho because the P-value is less than the significance level. OD. Fail to reject Ho because the P-value is less than the significance level. (d) Interpret the decision in the context of the original claim. O A.…
Please answer the Q2 and Q3.
For least-squares to work well, we need: ) the relationship between x and y to be non-linear. residuals to be Uniformly distributed. ) the residuals to have a mean of zero. the residuals to be correlated with the explanatory variable.
With an American penny, the likelihood of getting H when it is spun on edge is 0.3. If X is the random variable where X(H ) = 1, X(T ) = −1, find the expected value E(X), the variance, Var(X), and express X in its standard form.
The differentiation approach to derive the maximum likelihood estimator (mle) is not appropriate in all the cases. Let X₁, X2,,X₁ be a random sample of size n from the population of X. Consider the probability function of X fe-(2-0), if 0
Suppose the random variable, X, follows a geometric distribution with parameter 0 (0 < 0 < 1). Let X₁, X2,..., X be a random sample of size n from the population of X. (a) Write down the likelihood function of the parameter. (b) Show that the log likelihood function of depends on the sample only through Σj=1 Xj. (c) Find the maximum likelihood estimator (mle) of 0. (d) Find the method of moments estimator (mme) of 0.
(4) Consider n i.i.d. samples of X ~ N(µ,0²). Find the maximum likelihood estimate of o?.
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Suppose the data f(x) = α xa 5, 2, 3 was drawn independently from such a distribution. Find the maximum likelihood estimate (MLE) of a.