Suppose Y; = B1x; + €;, i = 1, ...,n. In this equation x is non-random, ß1 is a parameter (unknown but not random), e ~ N(0, 0), and €1,..., En are independent. Find the MLE of o². Is it unbiased? If not adjust it to be unbiased.
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- A paper investigated the driving behavior of teenagers by observing their vehicles as they left a high school parking lot and then again at a site approximately 1 2 mile from the school. Assume that it is reasonable to regard the teen drivers in this study as representative of the population of teen drivers. Amount by Which Speed Limit Was Exceeded MaleDriver FemaleDriver 1.3 -0.1 1.3 0.4 0.9 1.1 2.1 0.7 0.7 1.1 1.3 1.2 3 0.1 1.3 0.9 0.6 0.5 2.1 0.5 (a) Use a .01 level of significance for any hypothesis tests. Data consistent with summary quantities appearing in the paper are given in the table. The measurements represent the difference between the observed vehicle speed and the posted speed limit (in miles per hour) for a sample of male teenage drivers and a sample of female teenage drivers. (Use μmales − μfemales.Round your test statistic to two decimal places. Round your degrees of freedom down to the nearest whole number. Round your p-value to…2- An expert estimates that the distribution parameter for durability times of parts produced with machine A in the factory is different from the distribution parameter for durability times of parts produced with machine B. Durability times of 4 parts produced from machine A and 4 parts produced from machine B are given below. Find the Mann-Whitney U value by using these data. a) 18 B) 6 NS) 16 D) 20 TO) 12Assume that as a portfolio manager the beta of your portfolio is 1.15 and that your performance is exactly on target with the SML data under condition 1. If the true SML data is given by condition 2, how much does your performance differ from the true SML? (1) RFR = 0.0625 Rm(proxy) = 0.12 (2) RK = 0.078 Rm(true) = 0.10
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