prove the following generalization of the variance fomula varla X + by] =a² var[X] + b²var[Y] + 2abcov[X, Y].
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- Consider the following regression model: Yi = B1 + B2X2i + ß3X3i + ß4X4i + ui Using the model above show that the maximum likelihood estimator for the variance, var (ui||X2i, X3i, B4X4i), is biased (be sure to comment of the nature of the bias).Q. Let the joint pmf of x and y be defined by f (x,y) = (x+y)/32 where x = 1,2 and y = 1,2,3,4Suppose that a random man's weight from a certain population is M~ Normal (μ = 200, o²49) and a random woman's weight is W ~ Normal( 140, o² = 25). If M and W are independent, what is the variance of the difference between a man's weight and a woman's weight, i.e. Var (M-W)? (a) 340 (b) 24 (c) 140 (d) 200 (e) None of the above
- Many properties of the fabric used in different textiles, such as sheets and clothing, are influenced by whether the diameter of yarn used in the creation of the textile is consistent. Therefore, various methods can be used to measure the diameter of yarn at specified intervals, such as every 2mm, to determine the consistency of the diameter. These measurements are normally distributed. Suppose that one textile manufacturer will not use any yarn in which the variance of the diameters is greater than 0.0009mm. In order to ensure that the yarn is usable, the diameter of a length of yarn is measured at 400 random intervals. The variance of those measurements is found to be 0.000992mm. Does this evidence provide support that the batch of yarn is unusable by the manufacturer? Use a 0.005 level of significance. Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the variance of X.What is the variance of a continuous random variable X whose probability density is
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