Question

16. Problem 16. Consider a composite system characterized by a joint probability density function given by, def The constant ξ is a real normalization factor and pxy is defined on the two-dimensional planar region DCartesian def where Rt denotes the set of strictly positive real numbers. a) Define the set Dpolar representing DCartesian recast in polar coordinates (r, ); b) Performing a change of coordinates (namely, from Cartesian to polar coordinates), find the expression of the new joint probability density function pRe (r, 0); c) Find the numerical value of the normalization factor ξ; d) Using the marginalization technique, find the expression of the marginal probability density function px (a) and specify its domain of definition; e) Verify in an explicit manner the ρχ (z) is properly normalized f) Do you expect that py () equals px (a)? Please, justify your answer in a clear manner.

Answer 1

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