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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.
For a candidate who guesses at all answers, find the mean and variance for the random variable X, the number of correct answers.
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a) Test whether there is a difference between attitudes in the 2 cities. Use a 95% alpha. b) What does your result say about attitude consistency across cities?
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