Question: Please show full working Problem 1 Let R ~ Uniform(0, 1) and T ~ Uniform(-, ) be independent random variables. Define a transformation from (R,

Please show full working Problem 1 Let R ~ Uniform(0, 1)

Please show full working

Problem 1 Let R ~ Uniform(0, 1) and T ~ Uniform(-", ") be independent random variables. Define a transformation from (R, T) to the new variables X = R cos T and Y = R sin 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? To think about by yourself, not for submission: Is it possible to make sense of the conditional distribution of X given that Y = 0

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