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

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Publisher:Patrick M. Carey

Chapter9: Getting Started With Javascript: Creating A Countdown Clock

Section: Chapter Questions

Problem 16CP1

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