/sci/ - Science & Math

[Anonymous No.5881007]

probability class notes:

>let x=0,1,... , 0<p<1 , r integer >0

sum, from x=0 to x=infinity

( r+x-1 choose x )

times

((1-p)e^t)^x

times

(1-(1-p)e^t)^r

equals

1

>why?

infinite_sum ( r+x-1 choose x ) * ((1-p)e^t)^x * (1-(1-p)e^t)^r = 1

[Anonymous No.5881022]

why not

[Anonymous No.5881289]

LaTeXing that

Let [; x=0,1,...; p\in (0,1); r>0, r\in \mathbb{Z} ;]
[; \sum\limits_{x=0}^\infty {r+x-1 \choose x}((1-p)e^t)^x(1-(1-p)e^t)^r=1 ;]

[Anonymous No.5882806]