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Assigned 10/16/06, Due 10/26/06 (by 4:30 in dropbox in MSEE 330)
1. An exam is taken by 20 students and the results are
(a) Plot a histogram of the grades with bin size of 10, i.e., plot the number of grades between
99 and 90, 89 and 80, 79 and 70,..., 29 and 20.
(b) Compute estimates of the mean and variance using a button on your calculator, a formula
from the text or any other source you like (say what you used).
(c) Assuming that the grades are random samples of a Gaussian random variable with mean
and variance as in part b),
nd the ranges which correspond to grades of A,B,C,D, and
F as discussed in class. Compare the probability of each grade based on the Gaussian
assumption with the actual fraction of scores in each range.
(d) Instead of assigning grades as in part c),
nd the ranges which correspond to grades of
A,B,C,D, and F such that the fraction of scores in each range is
the same as the
probability based on the Gaussian assumption. Compare the ranges of scores based on
the Gaussian assumption (from part c)) with the ranges found in this way. Note: since
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 Fall '08
 GELFAND
 Probability theory, quantization error

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