Q1.The random variables X1,…Xn are independent and sampled from a distribution whoseprobability density function,f(x;A),for入>0 an unknown parameter,is such thatf(r;A)x Ax exp(-Ax2)ifx≥0，andf(x;)=0ifx<0.(a)Determine the full probability density function,f(z;A).[5](b)Determine the maximum likelihood estimator of入.[4]The following sample of X1,...Xn is collected,where n 5:2.30,1.99,1.49,0.62,2.53.A Bayesian statistician decides to assume Jeffreys'prior distribution for入.(c)Determine the posterior distribution of.[6]
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