Consider a random sample X1,...,Xn (n > 2) from Beta(θ,1), where we wish to estimate the parameter θ. (a) Find the MLE θˆ and write it as a function of T = − ∑ni=1 log Xi. (b) Find the sampling distribution of T = − ∑ni=1 log Xi . (Hint: First find the distribution of Ti = − log Xi .)
Consider a random sample X1,...,Xn (n > 2) from Beta(θ,1), where we wish to estimate the parameter θ. (a) Find the MLE θˆ and write it as a function of T = − ∑ni=1 log Xi. (b) Find the sampling distribution of T = − ∑ni=1 log Xi . (Hint: First find the distribution of Ti = − log Xi .)
Consider a random sample X1,...,Xn (n > 2) from Beta(θ,1), where we wish to estimate the parameter θ. (a) Find the MLE θˆ and write it as a function of T = − ∑ni=1 log Xi. (b) Find the sampling distribution of T = − ∑ni=1 log Xi . (Hint: First find the distribution of Ti = − log Xi .)
Consider a random sample X1,...,Xn (n > 2) from Beta(θ,1), where we wish to estimate the parameter θ.
(a) Find the MLE θˆ and write it as a function of T = − ∑ni=1 log Xi.
(b) Find the sampling distribution of T = − ∑ni=1 log Xi .
(Hint: First find the distribution of Ti = − log Xi .)
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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