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Could you help me with these questions please? 3. Let X1, X2, ..., Xn be generated by a Normal distribution where u is known and

Could you help me with these questions please?

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3. Let X1, X2, ..., Xn be generated by a Normal distribution where u is known and does not have to be estimated by X. We showed in class that 6? =1ET, (X, -X) is biased for o2. Show that o? = = ET-,(X; - #)? is unbiased for o2. 4. Based on the random sample X1 = 6.3, X2 = 1.8, X3 = 14.2, and X4 = 7.6, (a) use the method of maximum likelihood to estimate the parameter @ in the uniform pdf fx (x; 0) = =, Oxs0 (b) Suppose the random sample above represents the two-parameter uniform pdf fx (x; 01, #2) = 1 02 - 01' Find the maximum likelihood estimates for 6, and 02

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