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problem 6 gamma distribution is defined by its density function...

Question: problem 6 gamma distribution is defined by its density function...

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Problem 6. Gamma distribution is defined by its density function T(a) when t 0 and 0 otherwise. Here, θ is unknown parameter, a is a known param- eter Г(a) is a normalization constant (like in chi-square distribution discussed in class, see also p. 99 of the textbook) a) Check that Gamma distribution can be written in the exponential form. b) Use this fact to give a sufficient statistic for θ (you can do it with no additional computations after part a c) Give examples of two more different sufficient statistics for θ.

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