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# 13 Assumc random variable X follows the Beta(a,b) distribution with pdfT(a + 6) f(r) = 1"-1(1-1)-1 0 <I <1 a > 0,6 > 0. T(a)r(6)Calculate the mcan ...

## Question

###### 13 Assumc random variable X follows the Beta(a,b) distribution with pdfT(a + 6) f(r) = 1"-1(1-1)-1 0 <I <1 a > 0,6 > 0. T(a)r(6)Calculate the mcan valuc E(X) of X. To gencrate random variable X from this distribution bascd thc Acccpt-Reject mcthod_ aSSuMIC 3,6 use U(0,1) (Uniform distribution on [0, 1]) as proposal or an instrumental distribution: Fiud the possible minimum value of M for the Accept-Reject method and calculate the thcorctical acceptance ratc for this simulatio

13 Assumc random variable X follows the Beta(a,b) distribution with pdf T(a + 6) f(r) = 1"-1(1-1)-1 0 <I <1 a > 0,6 > 0. T(a)r(6) Calculate the mcan valuc E(X) of X. To gencrate random variable X from this distribution bascd thc Acccpt-Reject mcthod_ aSSuMIC 3,6 use U(0,1) (Uniform distribution on [0, 1]) as proposal or an instrumental distribution: Fiud the possible minimum value of M for the Accept-Reject method and calculate the thcorctical acceptance ratc for this simulation; Write an R program (0 generate random sample of size NSim 10 ' using the method stated part (6) Caleulate the sample mcnn of your generatel random sample and compare i t0 thie thevretical [ean value E(X obtained in (a). Compare your prOgram with the built-in R functions rbeta using histograms with superimposed true density curve, Include your R code and graphs,

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