Convolutions CS1-04 Joint distributions

I am trying to follow how the Summation of x=0 to z (zCr)*lambda^x*mu^(z-x) returns (lamda+mu)^z
See link to the question
https://getgreattips.wordpress.com/2021/12/22/convolutions/

 

See here: https://en.wikipedia.org/wiki/Binomial_theorem#Statement

It's just a standard piece of maths you'd be expected to spot, much like you're expected to spot when the density function of a distribution crops up.

 

Thanks but not very helpful

 

No problem.

Why is it not helpful? Do you not understand why the binomial theorem is true? I assumed you'd be ok with that, but you just hadn't spotted it applied here.

If you don't know why expressions like (x + y)^n expand this way, then read the 'Example' under 'Combinatorial proof' under the 'Proofs' section of the wikipedia page I linked: https://en.wikipedia.org/wiki/Binomial_theorem#Example