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Probability Density Function - Complex Gaussian Noise

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Referencing the attached:

NOTE:
The solution for part B is highlighted within the attached file. Re-stated here it is:

p(I) = ( 1 / < I > ) exp ( - I / < I > )

I'm not sure how.

Part a, is essentially:
Integral (infinity, 0) p(I, theta) di.

which according to my calculation equals:
- 1
--- exp (-I/2*sigma^2) evaluated at (infinity and 0)
I * pi

Now if I plug in infinity and zero for I i get (infinity - zero). Seems odd!!

Refer to the attachment for more information.

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The expert examines probability density functions and complex Gaussian Noise. The solution is given step-by-step equationally.

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Probability Density Function - Complex Gaussian Noise
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a) I think you have done some error in integrating; I am getting a better solution.

I will use "@" for phase angle theta, and "~" for ...

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