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Let X be a random variable with pdf f(x) = pfi(x) + (1 - p)f2(x), IT which is a mixture of two pdf's fi(x) and f2(x) where f1 (2) = 1+(-0₁) is a pdf of Cauchy distribution and |f2(x)=√√/2 is a pdf of a' normal distribution. The parameter of interest is 0₁ and 02 to be estimated from the data of size n, X₁X,Xn. For simplicity, we assume p = 0.2 and n = 500. (a) Write the likelihood function L(0₁.02) and its log-likelihood 1(01,02) = log(L(01,02)). (b) Write R code to generate the data of n = 500 from the mixture pdf f(x) with 0₁ = 10 and 0₂= 3. - (c) With the data generated above, write an R function, like (0₁02), for 1(01,02). data (a) Tuis

Let X be a random variable with pdf f(x) = pfi(x) + (1 - p)f2(x), IT which is a mixture of two pdf's fi(x) and f2(x) where f1 (2) = 1+(-0₁) is a pdf of Cauchy distribution and |f2(x)=√√/2 is a pdf of a' normal distribution. The parameter of interest is 0₁ and 02 to be estimated from the data of size n, X₁X,Xn. For simplicity, we assume p = 0.2 and n = 500. (a) Write the likelihood function L(0₁.02) and its log-likelihood 1(01,02) = log(L(01,02)). (b) Write R code to generate the data of n = 500 from the mixture pdf f(x) with 0₁ = 10 and 0₂= 3. - (c) With the data generated above, write an R function, like (0₁02), for 1(01,02). data (a) Tuis

New Perspectives on HTML5, CSS3, and JavaScript
New Perspectives on HTML5, CSS3, and JavaScript
6th Edition
ISBN:9781305503922
Author:Patrick M. Carey
Publisher:Patrick M. Carey
Chapter9: Getting Started With Javascript: Creating A Countdown Clock
Section: Chapter Questions
Problem 16CP1
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Insert Design Layout Painter S Cambria English (India) 12 ▼ References Mailings Review View BI U abe X₂ X² A. ab A- Font A A Q Search Aa A :3 2023-f1-7685-8685 - Word WPS PDF Paragraph 2. Let X be a random variable with pdf f(x) = pf1(x) + (1 − p)ƒ2(x), which is a mixture of two pdf's fi(x) and ƒ2(x) where f1(x) = // 1 (x-02)² - 2 = L Tell me what you want to do... e ¶¶AaBb CcD AaBb CcD AaBbCc AaBbCcD AaB 1 Normal ¶ No Spac... Heading 1 Heading 2 Title Cauchy distribution and f2(x) 1 √2T is a pdf of a' normal distribution. The parameter of interest is ₁ and ₂ to be estimated from the data of size n, X₁, Xn,,Xn. For simplicity, we assume p = 0.2 and n = 500. (a) Write the likelihood function L(0₁,02) and its log-likelihood 1(0₁,02) = log(L(01,02)). (b) Write R code to generate the data of n = 500 from the mixture pdf f(x) with 0₁ = 10 and 0₂= 3. It (c) With the data generated above, write an R function, like (0₁,02), for I(0₁,02). (d) Write an R code to show the 3-D plot of 1(01,02). (e) Write an R code to show the contour plot of 1(0₁,02). (f) Using the numeric method, write an R code to find the MLE (maximum likelihood estimates) of 0 = = (0₁,0₂). (2) Write R code to implement cimnla hacic stochastic C 3. Following the same setup and/or data generated from Problem 1 and Problem 2, answer the questions below using simulation based methods with a sequence of n = 104 iterations: 1 π 1+(x−0₁)² is a pdf of X Styles wwwww search to find the (((( 0 W ENG US 5 Mr. Dasharath Find - ab Sac Replace Select - Editing 20 18 04-11-2023
Transcribed Image Text:Insert Design Layout Painter S Cambria English (India) 12 ▼ References Mailings Review View BI U abe X₂ X² A. ab A- Font A A Q Search Aa A :3 2023-f1-7685-8685 - Word WPS PDF Paragraph 2. Let X be a random variable with pdf f(x) = pf1(x) + (1 − p)ƒ2(x), which is a mixture of two pdf's fi(x) and ƒ2(x) where f1(x) = // 1 (x-02)² - 2 = L Tell me what you want to do... e ¶¶AaBb CcD AaBb CcD AaBbCc AaBbCcD AaB 1 Normal ¶ No Spac... Heading 1 Heading 2 Title Cauchy distribution and f2(x) 1 √2T is a pdf of a' normal distribution. The parameter of interest is ₁ and ₂ to be estimated from the data of size n, X₁, Xn,,Xn. For simplicity, we assume p = 0.2 and n = 500. (a) Write the likelihood function L(0₁,02) and its log-likelihood 1(0₁,02) = log(L(01,02)). (b) Write R code to generate the data of n = 500 from the mixture pdf f(x) with 0₁ = 10 and 0₂= 3. It (c) With the data generated above, write an R function, like (0₁,02), for I(0₁,02). (d) Write an R code to show the 3-D plot of 1(01,02). (e) Write an R code to show the contour plot of 1(0₁,02). (f) Using the numeric method, write an R code to find the MLE (maximum likelihood estimates) of 0 = = (0₁,0₂). (2) Write R code to implement cimnla hacic stochastic C 3. Following the same setup and/or data generated from Problem 1 and Problem 2, answer the questions below using simulation based methods with a sequence of n = 104 iterations: 1 π 1+(x−0₁)² is a pdf of X Styles wwwww search to find the (((( 0 W ENG US 5 Mr. Dasharath Find - ab Sac Replace Select - Editing 20 18 04-11-2023
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