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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 1,3,0,00, 2, 22,0,1,2,0 1,1,0,1,1, 3, î021, 3. i 20.3.0, 2, i, (a) (i) Find and s for this sample. (ii) 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 inaximum likelihood estimate of θ is 6 1 - fo/n, where fo is the umber of observed 0s in the sample (iii) Find the standard error of θ. (iv) Calculate a 95% confidence interval for based ono/2 n-I - 1,036520 6 23 2 二 100-850 9 9 sampe mcan e 50 12varle ar 1 2 25 01073 dra?

NOTE: DO PART b) ONLY

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