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Let X And Y Be Independent Continuous Random Variables That Are U(-1,1) (i.e., They Have Uniform Dis

Let X and Y be independent continuous random variables that are
U(-1,1) (i.e., they have uniform distribution over the interval
(-1,1)). Note that this implies that their CDFs are
F_{x}(x)=(1/2)(x+1) for -1 < x < 1 and
F_{Y}(y)=(1/2)(y+1) for -1 < y < 1 (These are also
equal to 0 over an appropriate interval and 1 over another
appropriate interval).

Let V = max(X,Y) and W= 1-2x^{2} (a) Show work by hand
to confirm that the PDF of V is f_{V}(v)=(1/2)(v+1) for -1
< v < 1 (and it is zero otherwise). Start your work by
finding the CDF F_{V}(v). (b) Show work by hand to confirm
that the mean is
v = E[V] = (1/3). (c) Show work by hand to confirm the PDF of W is
for -1 < w < 1 (and it is zero otherwise). Start your work
by finding the CDF of F_{W}(w). (d) Show your work by hand
to confirm that the mean is
W = E[W} = (1/3). You may need to do a substitution to help you do
an appropriate integral here.