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2. A discrete random variable X has the following pmf A random sample of size n 30 produced the following observations: (a)) Find and s for this sample Find E(X) and var(X) (iii) Find the method of moments estimate of θ (iv) Find the standard error of this estimate. (b) (i) Find the likelihood function (ii) Show that the maximum likelihood estimate of θ is -1 fo/n, where fo is the number of observed 0s in the sample. (iii) Find the standard error of θ (iv) Calculate a 95% confidence interval for θ based on θ.

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As per HOMEWORKLIB POLICY, you have to upload the second subpart as another question and thus I am only answering 1st subpart.

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