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Assigned 9/22/11, Due 10/4/11 (by 4:30 in dropbox in MSEE 330)
1. Text, problem 3.25, page 133
2. Text, problem 3.39, page 134
3. Dwightand Jim are having a snowball ±ght.
and
are the positions, in feet (to left and
right), which their respective snowballs land relative to the target. We have that Dwight²s
snowballs have a pdf
Jim has more consistent aim, but aims a little to the right, so that
(a) What are the mean and variance of
and
?
(b) Let
and
be the events that that Dwight and Jim, respectively, throw a good
toss (within 0.5 feet of the target). Find the conditional pdf, mean and variance for
given
, and for
given
(c) Suppose it is not known whose snowball is tossed, and the probabilitythat the snowball
comes from Dwight or Jim are equally likely. Let
denote the position where the
snowball lands relative to the target. Find the pdf, mean and variance of . Is the