Typical mistakes on Test 3:
Problem 1: found the value of the Lagrange multiplies, but the
problem is not solved: we still need to find the values of the
unknowns x_{1} and x_{2}
Problems 2 and 3:
* variance is already the square of standard deviation, so if
variance is 20, there is no need to square it further
* some students forgot the second constraint: that the sum of the
weights should be 1
* since there are only two investments, constraints form the
system of 2 linear equations with two unknowns, from which we can
easily determine both weights
Problem 5: robust means less vulnerable to outlier; if Bill Gates
walks into a bar, the mean (l^{2}) income grows to
millions, but the median (l^{1) remains practically
unchanged
Problem 8: to compare the final results, we need to multiply, not
add; for example, if both times we had a 10% increase, then each
original dollar first grows to $1.10, then to $1.10 * 1.10 = $1.21
Comparing the sum of interests can lead to a wrong conclusion. For
example, suppose that fund A gives 10% every year, while fund B gave 20.5%
the first year and no increase the second year. The sum of
percentages is larger for fund B. However, $1 invested in fund A
leads to $1.21, while $1 invested in fund B only leads to $1.205,
which is smaller than $1.21.
Problem 10: our justification for peak-end rule used
shift-invariance, scale-invariance, associativity, and idempotence
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