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Suppose that X is a discrete random variable with ?(? = 1) = ? and ?(?...

Suppose that X is a discrete random variable with ?(? = 1) = ? and ?(? = 2) = 1 − ?. Three independent observations of X are made: (?1, ?2, ?3) = (1,2,2).

a. Estimate ? through the sample mean (this is an example of the “method of moment” for estimating a parameter).

b. Find the likelihood function and MLE for ?.

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