# Question: If V1 V2 Vn and W1

If V1, V2, . . . , Vn and W1, W2, . . . , Wn are independent random samples of size n from normal populations with the means µ1 = α + β and µ2 = α – β and the common variance σ2 = 1, find maximum likelihood estimators for α and β.

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If V1, V2, . . . , Vn1 and W1, W2, . . . , Wn2 are independent random samples of sizes n1 and n2 from normal populations with the means µ1 and µ2 and the common variance σ2, find maximum likelihood estimators for µ1, ...Show that the mean of the posterior distribution of M given in Theorem 10.6 can be written as That is, as a weighted mean of x and µ0, where Not counting the ones that failed immediately, certain light bulbs had useful lives of 415, 433, 489, 531, 466, 410, 479, 403, 562, 422, 475, and 439 hours. Assuming that these data can be looked upon as a random sample from ...Records of a university (collected over many years) show that on the average 74 percent of all incoming freshmen have I.Q.’s of at least 115. Of course, the percentage varies somewhat from year to year, and this variation ...Fill in the details that led from the probability on page 325 to the confidence-interval formula of Theorem 11.10.Post your question