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Suppose that (U,V) is uniformly distributed on the unit square. That is, suppose that the pair has joint pdf
f(u,v)=I[0<u<1 and 0<v<1]
Consider the random variable T=U+V
a) Find the cdf of T. (You can find different "formulas" for F(t) depending upon how t compares to the values 0,1, and 2. Once you identify the set of (u,v) with total less than or equal to t, simple geometry can be used to find the value of F(t).)
b) Use a) and find the pdf of T.
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