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4. (20 points) Suppose that we have two independent random samples: X,..., Xn are exponential(0), and Y, ..., Y are exponential(). (a) Find the

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4. (20 points) Suppose that we have two independent random samples: X,..., Xn are exponential(0), and Y, ..., Y are exponential(). (a) Find the LRT of Ho : 0 = versus Ho : # . (b) Show that the test in part (a) can be based on the statistic T = (c) Find the distribution of T when H is true. = Xi+Yi*

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