Characteristic equation of binomial random variable

  • Thread starter sinned4789
  • Start date
  • #1
sinned4789
7
0

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
9,568
774
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.
 

Suggested for: Characteristic equation of binomial random variable

Replies
5
Views
245
Replies
4
Views
133
Replies
9
Views
482
Replies
11
Views
457
Replies
1
Views
109
Replies
16
Views
461
Replies
2
Views
365
Replies
2
Views
438
Replies
1
Views
330
Replies
6
Views
1K
Top