1 (X₁, To test a proportion of defective items one draws a sample X₁ = population with an unknown € (0, 1). Give the likelihood function of the sample. (ii) Find the m.l.e. and MLE of 0. Hint. (i) We can write the density f(x|0) of each r.v. X₁ as x = 0,1 0² (1 - 0)¹-²1(0,1) (0), 0, otherwise. f (x 0 ) = {' Thus, the likelihood function is fn(Xn|0) = 0° (1 –0)”°1(o,n)(0) where 0 : = x₁ + ... + än. (Explain why.) (ii) The value of that maximizes the likelihood function is the same value that maximizes the log of fn (Xn0) since the log function is strictly monotone. So, let L(0) = lnfn (xn|0) = oln0 + (n − σ)ln(1 – 0). - Then, show that Xn) from a Bernoulli L'(0) = n(1-0),

1 (X₁, To test a proportion of defective items one draws a sample X₁ = population with an unknown € (0, 1). Give the likelihood function of the sample. (ii) Find the m.l.e. and MLE of 0. Hint. (i) We can write the density f(x|0) of each r.v. X₁ as x = 0,1 0² (1 - 0)¹-²1(0,1) (0), 0, otherwise. f (x 0 ) = {' Thus, the likelihood function is fn(Xn|0) = 0° (1 –0)”°1(o,n)(0) where 0 : = x₁ + ... + än. (Explain why.) (ii) The value of that maximizes the likelihood function is the same value that maximizes the log of fn (Xn0) since the log function is strictly monotone. So, let L(0) = lnfn (xn|0) = oln0 + (n − σ)ln(1 – 0). - Then, show that Xn) from a Bernoulli L'(0) = n(1-0),

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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