Problem 15   Due 3/7/01

The 1994 almanac lists the following as the
production of nuts in the United States on
a yearly basis for the three major nut crops:

Year    Pecans  Almonds Walnuts
        (1,000  (1,000  (1,000
        tons)   tons)   tons)
1980    91.8    264.4   197
1982    109.3   283.5   234
1985    122.2   375.6   219
1986    136.4   201.3   180
1987    131.1   519     247
1988    154.1   451.9   209
1989    125.3   394.7   229
1990    102.5   519.7   227
1991    149.5   385.8   259
1992    88      451.9   200

a). For this set of data calculate the mean annual
production of each type of nut, together with its
standard deviation.

b). Calculate the matrix of covariance between of 
the three types of nuts (the off-diagonal values will
be the covariances of the three possible pairs).

c). Using the information obtained in part a and b
rather than the original data set, calculate the mean
and standard deviation of the fraction of nuts consisting
of pecans, e.g., fraction = pecans/(pecans+walnuts+almonds).

d). Compare the answer in part c to that which would
be calculated directly from the yearly data.