57. According to quantum mechanics, the x- and y-coordinates of a par- ticle confined to the region R = [0, 1] × [0, 1] are random variables with joint probability density function [C sin²(2rlx) sin²(2rny) if (x, y) e R p(x, y) = otherwise The integers e and n determine the energy of the particle, and C is a constant. (a) Find the constant C. (b) Calculate the probability that a particle with e = 2, n = 3 lies in the region [0, 4] × [0, £].

Q: (a) fxy(x, y) = (b) fyx (x, y) =

A:

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A: (As per bartleby guideline, for more than 3 subparts only 3 will be solved, Please upload another…

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A: As per the guidelines of the Bartleby, solution of only first 3 parts are given.

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