Question about continuous and discrete moment generating functions.

  • Thread starter The1TL
  • Start date
  • #1
26
0

Homework Statement



is there a continuous real valued variable X with mgf: (1/2)(1+e^t)

Homework Equations





The Attempt at a Solution


I've noticed that this is the mgf of a bernoulli distribution with p =1/2. But since bernoulli is a discrete distribution, does that disprove that there is a continuous variable with that mgf?
 

Answers and Replies

  • #2
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,722

Homework Statement



is there a continuous real valued variable X with mgf: (1/2)(1+e^t)

Homework Equations





The Attempt at a Solution


I've noticed that this is the mgf of a bernoulli distribution with p =1/2. But since bernoulli is a discrete distribution, does that disprove that there is a continuous variable with that mgf?

There is a theorem that two cdfs are the same if and only if their characteristic functions are the same; in other words, a characteristic function can belong to only one cdf. Of course, the mgf is the characteristic function at an imaginary argument, so the result still applies. Just Google "characteristic function" for more details.
 

Related Threads on Question about continuous and discrete moment generating functions.

Replies
15
Views
3K
  • Last Post
Replies
17
Views
3K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
18
Views
1K
Replies
6
Views
2K
  • Last Post
Replies
4
Views
718
Replies
3
Views
1K
Replies
8
Views
3K
Top