4X + 3; V 2. Consider the following random variables derived from Ap, which you obtained above (I'm going to call it X now to simplify notation, i.e. X = Ap). S = X + 2; Z 2X; W W + 2S. In each case, give an estimate of the mean and variance of the new random variable (these are estimates because the mean and variance obtained in the first part of the question are estimates; if those were population values, you could compute population values for the new random variables). You can just assign a name to the mean and variance of U and give your answer as a function of that variable, eg. define the mean of U as , variance of U as vu, give answers as functions of u and v₁. Note that you don't have to do any data analysis to answer this question. You can obtain your answers by reasoning, applied to the mean and variance of Ap that you obtained earlier. If you find this non-transparent or have any doubts about your answers, you can actually construct the new variables and do the computations again from scratch. = = =

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