Question: Problem 1 Let R ~ Uniform(0, 1) and T ~ Uniform(-7, ) be independent random variables. Define a transformation from (R, T) to the new

Problem 1 Let R ~ Uniform(0, 1) and T ~ Uniform(-7,

Problem 1 Let R ~ Uniform(0, 1) and T ~ Uniform(-7, ") be independent random variables. Define a transformation from (R, T) to the new variables X = R cos T and Y = Rsin T. This is a smooth one-to-one transformation. 1 pts (a) What is the range of the transformation x = r cost, y = r sint (for t| 0? Why is this not the same as E[ X | T = 0] = ERT = 0 = E[R] = -, even though the events { Y = 0} and {7 = 0} are identical

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