Stat 5101, Fall 1999, (Geyer) First Midterm Solutions

# Stat 5101, Fall 1999, (Geyer) First Midterm Solutions - Up:...

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Up: Stat 5101 Stat 5101 (Geyer) Midterm 1 Problem 1 The correlation is given by So in order to calculate this we need to first do two subproblems. What is ? What is ? The second is simpler. By the addition rule for variances of uncorrelated random variables (the variance of a sum is the sum of the variances) For the first, we need the rule for taking a sum outside a covariance and the rule Thus A Comment You can if you like always use the formulas to calculate variances and covariances. They are, after all, valid formulas, so, if you don't make any mistakes, you can use them to get correct answers.

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But using these formulas are a bad idea in a problem like this. Note that the easy solution we give here does not involve means at all! If you do the problem the easy way, you cannot get an incorrect answer involving . If you do the problem using the formulas involving means and you make a mistake, the means won't cancel out. It's just much simpler if you use the rules for variances and covariances that don't involve means . if (as in this problem) the
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## Stat 5101, Fall 1999, (Geyer) First Midterm Solutions - Up:...

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