Ps3 | Physical chemistry homework help

5. A Poisson distribution is used to describe things like the number of drops

hitting you per minute in a light rain. Please use Mathematica to show that the Poisson probability distribution: λke−λ k!

is properly normalized; you will use two different methods:

a. Try to demonstrate this way:

∫ λke−λ k! ∞ ∂k b. Before you go too crazy, you should know that integration in pt. a won’t work. Try summing the distribution instead. Why does this approach reveal proper normalization while integration (pt. a) failed? Note, you may have to do some googling to see how to do a summation in Mathematica. c. Now that you know how to properly “work” the Poisson distribution, please calculate the average value ⟨k⟩. d. Also calculate ⟨k2⟩, and the variance ⟨k2⟩ − ⟨k⟩2. (10 pts) © 2023, Preston T. Snee This work is licensed under a Creative Commons Attribution- NonCommercial 4.0 International License.