There's a spider living on a wall of your living room that has a painting behind
which the spider likes to
hide. Figure 1 shows a diagram of the wall; it is 10 feet high and 10
After observing the spider for a while you determine that (1) it spends twice the time behind
the painting than on the rest of the wall, (2) it never crawls on the painting or leaves the wall,
(3) if it is not behind the painting then it is equally likely to be anywhere on the wall. Since
you cannot see it behind the painting, you assume that when it is there it is also equally likely
to be at any spot.
a. Model the position of the spider as a bivariate random variable and give its pdf.
b. Compute the pdf of the height at which the spider is located and sketch it.
c. Compute the conditional cdf of the height at which the spider is located, given that you can see it (i.e. it's not under the painting) and sketch it.
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