• Support PF! Buy your school textbooks, materials and every day products Here!

Characteristic equation of binomial random variable

  • Thread starter sinned4789
  • Start date
  • #1

Homework Statement


find the characteristic equation of a binomial variable with pmf p(x) =[tex]\frac{n!}{(n-k)!k!}[/tex]*p[tex]^{k}[/tex]*(1-p)[tex]^{n-k}[/tex]


Homework Equations


characteristic equation
I(t) = [tex]\sum[/tex]p(x)*e[tex]^{tk}[/tex]


The Attempt at a Solution


I(t) = [tex]\sum[/tex][tex]\frac{n!}{(n-k)!k!}[/tex]*(p[tex]^{k}[/tex]*(1-p)[tex]^{-k}[/tex]*e[tex]^{tk}[/tex])*(1-p)[tex]^{n}[/tex]

i am stuck on this series because i dont know what to do with the combination term.
 

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,535
751
In the definition

[tex]E(tX) = \sum_{k-0}^{n}\binom n k e^{tk}p^k(1-p)^{n-k}[/tex]

group the etk with the pk and then think about what the binomial expansion of (a + b)n looks like.
 

Related Threads on Characteristic equation of binomial random variable

  • Last Post
Replies
1
Views
1K
Replies
0
Views
7K
Replies
11
Views
2K
Replies
16
Views
2K
Replies
6
Views
646
Replies
3
Views
1K
Replies
12
Views
4K
Replies
4
Views
3K
Replies
5
Views
4K
Replies
8
Views
13K
Top