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A radio astronomer is studying the polarization of the 21-сm line emitted by a cloud of interstellar hydrogen gas. He fi
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A radio astronomer is studying the polarization of the 21-сm line emitted by a cloud of interstellar hydrogen gas. He fi
A radio astronomer is studying the polarization of the 21-сm line emitted by a cloud of interstellar hydrogen gas. He finds that the joint probability distribution for the parallel, A, and perpendicular, B, polarized radiation in some physically meaningful direction is given by , (Y2B2 p(A,B) exp[-B(A + y)/a?], 0 < A,B = q6 0 otherwise where a and y are positive parameters with units of intensity. a) Find p(A) and p(B). Sketch your results. b) Find the conditional probability density p(AB) and sketch your result. c) Are A and B statistically independent? Justify your answer.
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