5.6.8. Suppose a random sample of size n is drawn fromthe pdf1fy(y; 0)=0≤ y ≤ 0ᎾFind a sufficient statistic for 0.

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Answered: 5.6.8. Suppose a random sample of size…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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6.2.2 If (x₁, ..., xn) is a sample from a Bernoulli(0) distribution, where 0 = [0, 1] is unknown, then determine the MLE of 0. 6.2.3 If (x₁,...,xn) is a sample from a Bernoulli(0) distribution, where 0 = [0, 1] is unknown, then determine the MLE of 0².
6.4.5-T Assume that females have pulse rates that are normally distributed with a mean of u = 74.0 beats per minute and a standard deviation of o = 12.5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 78 beats per minute. The probability is 0.6255. (Round to four decimal places as needed.) b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 78 beats per minute. The probability is (Round to four decimal places as needed.)
answer With details pls. can you explain the difference between the E(Yn) E(Yi) and E(Y(n)) .
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7.4.1
5.65. Find the mean µ, variance o², and standard deviation o of each distribution: 2 3 8 (a) (b) X f(x) X f(x) 1/4 -2 1/3 1/2 1/4 -1 7 1/2 1/6
16. Let X, X2 X, be a random sample from a normal distribution, X, N(6, 25), and denote by X and S2 the sample mean and sample variance. Use tables from Appendix C to find each of the following: (a) P[3 < X < T. (b) P[L860< 3(X-6)/S]. (c) PIS <319375]
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.
2
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6.2.8. Let X be N(0, 0), 0 <0 < x. (a) Find the Fisher information I(0). (b) If X₁, X2,..., Xn is a random sample from this distribution, show that the mle ofis an efficient estimator of 0. (c) What is the asymptotic distribution of √(-0)?
24

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5.6.8. Suppose a random sample of size n is drawn from the pdf 1 fy(y; 0) = 0≤ y ≤ 0 Ꮎ Find a sufficient statistic for 0.