How to find pdf given moment generating function

AI Thread Summary
The moment generating function (MGF) provided, (e^t)/(2-e^t), corresponds to a unique probability distribution. This distribution is characterized by the probabilities p(k) = 1/2^k for k in the natural numbers, indicating that the random variable takes values 1, 2, 3, and so on, with probabilities 1/2, 1/4, 1/8, respectively. The discussion confirms that a bona fide MGF always maps to a unique distribution, negating the possibility of two different PDFs sharing the same MGF. Therefore, the PDF can be derived directly from the given MGF. Understanding the relationship between MGFs and their corresponding distributions is crucial in probability theory.
math-chick_41
Messages
34
Reaction score
0
Given that the moment generating function of a random variable is
(e^t)/(2-e^t) is there a way I can go backwards and find the pdf, or could 2 different pdf's have the same mgf?
 
Physics news on Phys.org
Any bonafide moment generating function always maps to a unique distribution.
The random variable for the moment generating functi`on that you have given takes values at 1,2,3...infinity with probability 1/2,1/4,1/8...ie p(k)=1/2^k for k in natural numbers and zero otherwise.
 

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
View full post »

Similar threads

I Proving a multivariate normal distribution by the moment generating function
Replies
5
Views
3K
I How to obtain moment bound from the importance sampling identity?
Replies
1
Views
2K
A Probability Density Function: Converting Experimental Observations to PDF
Replies
4
Views
2K
MHB Two normal independent random variables
Replies
2
Views
2K
I Does the generalized gamma distribution have a mgf?
Replies
1
Views
2K
MHB Distribution and Density functions of maximum of random variables
Replies
6
Views
4K
I Finding the pdf of a transformed univariate random variable
Replies
3
Views
2K
I CDF of summation of random variables
Replies
16
Views
2K
I The CDF from the characteristic function
Replies
36
Views
4K
I Given three random numbers between 0 and 1, how to evenly populate a sphere?
Replies
15
Views
2K

Hot Threads

Recent Insights

Back
Top