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let X1; X2; .......Xn be iid with Gamma (4;theta), where > 0. a)Find the MLE for P (X1 > 4). b)Find the asymptotic (limiting) distribution

let X1; X2; .......Xn be iid with Gamma (4;theta), where > 0.

a)Find the MLE for P (X1 > 4).

b)Find the asymptotic (limiting) distribution for the MLE in part (a)

c)Using the result of (b), construct an approximate (1-alpha) 100% condence interval for P (X1 > 4).

d) Given n = 100 and x = 3:838, use (c) to find an approximate 95% condence interval for P (X1 > 4). (Work required)

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