f(y0) = 30 y² exp{-0y³} provided y ≥0 where > 0 is a parameter. (a) Verify that f(y) belongs to an exponential family in canonical form. (b) Determine the maximum likelihood estimator of by solving the generalized moment equations as discussed in our coure notes titled Exponential Families and Maximum Likelihood Estimation.

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Suppose that Y1, . . . , Yn is a random sample from a population whose density function is

 

f (y\0) = 30 y² exp{-0 y³}
provided y 2 0 where 0 > 0 is a parameter.
(a) Verify that f(y|0) belongs to an exponential family in canonical form.
(b) Determine the maximum likelihood estimator of 0 by solving the generalized moment
equations as discussed in our coure notes titled Exponential Families and Maximum
Likelihood Estimation.
Transcribed Image Text:f (y\0) = 30 y² exp{-0 y³} provided y 2 0 where 0 > 0 is a parameter. (a) Verify that f(y|0) belongs to an exponential family in canonical form. (b) Determine the maximum likelihood estimator of 0 by solving the generalized moment equations as discussed in our coure notes titled Exponential Families and Maximum Likelihood Estimation.
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