MHB Probability generating function

Click For Summary
A probability generating function (pgf) can indeed have a constant term, but adding a constant alters its fundamental properties. Specifically, including a constant term means the sum of the coefficients would no longer equal one, disqualifying it as a pgf. The discussion emphasizes the importance of adhering to the definition of pgfs when considering modifications. Additionally, the derivative of a pgf can yield the same result even if a constant is added, but this would not maintain the pgf's integrity. Thus, while technically possible, adding a constant to a pgf is not appropriate.
Poirot1
Messages
243
Reaction score
0
My question is : can a pgf have a constant term?

The reason I ask is that I was asked to show the (time) derivative of a pgf was equal to some multiple of the pgf and hence show the pgf was as given. So naturally , I differentiated the given answer and showed it satisfied the equation. But surely I could stick a constant on the end and it would differentiate to the same thing.
 
Physics news on Phys.org
Poirot said:
My question is : can a pgf have a constant term?

The reason I ask is that I was asked to show the (time) derivative of a pgf was equal to some multiple of the pgf and hence show the pgf was as given. So naturally , I differentiated the given answer and showed it satisfied the equation. But surely I could stick a constant on the end and it would differentiate to the same thing.

The simple answer is yes.

The more complicated answer is: please post the actual question or more context.

Adding something onto a pgf will result in it no longer being a pgf, since the sum of the coefficients should be 1.

CB
 

Thread 'Two interesting number theory tricks'

First trick I learned this one a long time ago and have used it to entertain and amuse young kids. Ask your friend to write down a three-digit number without showing it to you. Then ask him or her to rearrange the digits to form a new three-digit number. After that, write whichever is the larger number above the other number, and then subtract the smaller from the larger, making sure that you don't see any of the numbers. Then ask the young "victim" to tell you any two of the digits of the...
View full post »

Similar threads

Graduate Deriving a Probability Generating Function for Independent Poisson Variables
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Understanding extinction probability in simple GWP
  • · Replies 1 ·
Replies
1
Views
2K
Probability Generating Functions
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad On the expected value of a sum of a random number of r.v.s.
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Does the generalized gamma distribution have a mgf?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Probability of misprints on each page
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Proving a multivariate normal distribution by the moment generating function
  • · Replies 5 ·
Replies
5
Views
3K
MHB Moment-Generating Function question
  • · Replies 1 ·
Replies
1
Views
1K
A game of roulette and generating functions
  • · Replies 3 ·
Replies
3
Views
1K
High School Distribution of particles, given a function
  • · Replies 2 ·
Replies
2
Views
1K