here in part a, i am using the integration by parts and beta function which are given above. for part c we will use MCMC techniques which is best to estimate such type of integration. i will perform part c by using R sofyware but i will describe all steps which i will used. here it is not easy to use for or while loop therefore we will use hit or miss method for start n=100, using R software
here note that x is random then values may be some random but will be approximately equal. therefore we can choose n=320 and estimated value of beta fn is 0.1601375.
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