Question: I need help on this statistics question. The question is specified as below. Thanks! Let *. .... I be an iid sample from and exponential

I need help on this statistics question. The question is specified as below. Thanks!

Let *. .... I be an iid sample from and exponential distribution with mean !) . ( a ) Let * = -` . = AL . Derive the joint pdf of Y . ... Y . ( Hint : find pdf of Y, first ) . ( b) It is easy to see that the sampling distribution of > Y, follows a Gamma( a , B ) . 1 = 1 determine the value of a and B . SX , ( C ) Explain why 1 =] O - is a pivotal quantity for deriving a Cl for O . ( d ) Now , suppose "1 = 10 and the average of the observed *. ... *, * = 2 . Use the pivotal method to derive and compute a 95% CI ( interval estimate ) for O . ( e ) Derive and compute the method of moments estimate of ! . ( 1) Derive the log - likelihood function for estimating @ and compute the maximum* likelihood estimate of 8

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