Q7. Let X1, X2, ... Xn be an independent random sample from the distribution with p.d.f. f(x;p) = P(1 – p)*, x = 0,1,2,

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Q7 Let X1 X2 Xn Be An Independent Random Sample From The Distribution With P D F F X P P 1 P X 0 1 2 1 (87.47 KiB) Viewed 14 times

Q7. Let X1, X2, ... Xn be an independent random sample from the distribution with p.d.f. f(x;p) = P(1 – p)*, x = 0,1,2, ... , where 0 <p<1. (i) Find a complete and sufficient statistic of p; (5 marks) (ii) Find the UMVUE of p. (5 marks) Q8. One observation is taken on a discrete random variable X with p.d.f. f(x; 0) in the fol- lowing table, where 0 € {1,2,3}. f(x; 1) f(x; 2) f(x; 3) 0 1/3 1/4 0 1 1/3 1/4 0 2 0 1/4 1/4 3 1/6 1/4 1/2 4. 1/6 0 1/4 Find the MLE of e. (5 marks)