Mixing
Finding Moment Generating Function from mean and variance [closed]
Suppose you have a random variable X whose moments are given by $E(X^n) = n!$.
Find the moment generating function for $X$.
Is it possible to find MGF or the probability distribution function of $X$ given mean and variance?
moment-generating-functions
edited Jan 1 at 6:44
Bertrand Wittgenstein's Ghost
354114
asked Jan 1 at 4:39
sample buffersample buffer
1
closed as off-topic by Eevee Trainer, heropup, Shailesh, mrtaurho, José Carlos Santos Jan 1 at 12:08
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, heropup, Shailesh, mrtaurho, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
Suppose you have a random variable X whose moments are given by $E(X^n) = n!$.
Find the moment generating function for $X$.
Is it possible to find MGF or the probability distribution function of $X$ given mean and variance?
moment-generating-functions
edited Jan 1 at 6:44
Bertrand Wittgenstein's Ghost
354114
asked Jan 1 at 4:39
sample buffersample buffer
1
closed as off-topic by Eevee Trainer, heropup, Shailesh, mrtaurho, José Carlos Santos Jan 1 at 12:08
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, heropup, Shailesh, mrtaurho, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
For the second question: obviously not.
– kimchi lover
Jan 1 at 4:50
add a comment |
Suppose you have a random variable X whose moments are given by $E(X^n) = n!$.
Find the moment generating function for $X$.
Is it possible to find MGF or the probability distribution function of $X$ given mean and variance?
moment-generating-functions
edited Jan 1 at 6:44
Bertrand Wittgenstein's Ghost
354114
asked Jan 1 at 4:39
sample buffersample buffer
1
Suppose you have a random variable X whose moments are given by $E(X^n) = n!$.
Find the moment generating function for $X$.
Is it possible to find MGF or the probability distribution function of $X$ given mean and variance?
moment-generating-functions
moment-generating-functions
edited Jan 1 at 6:44
Bertrand Wittgenstein's Ghost
354114
asked Jan 1 at 4:39
sample buffersample buffer
1
edited Jan 1 at 6:44
Bertrand Wittgenstein's Ghost
354114
asked Jan 1 at 4:39
sample buffersample buffer
1
edited Jan 1 at 6:44
Bertrand Wittgenstein's Ghost
354114
edited Jan 1 at 6:44
Bertrand Wittgenstein's Ghost
354114
edited Jan 1 at 6:44
Bertrand Wittgenstein's Ghost
354114
354114
asked Jan 1 at 4:39
sample buffersample buffer
1
asked Jan 1 at 4:39
sample buffersample buffer
1
asked Jan 1 at 4:39
sample buffersample buffer
1
1
closed as off-topic by Eevee Trainer, heropup, Shailesh, mrtaurho, José Carlos Santos Jan 1 at 12:08
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, heropup, Shailesh, mrtaurho, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Eevee Trainer, heropup, Shailesh, mrtaurho, José Carlos Santos Jan 1 at 12:08
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, heropup, Shailesh, mrtaurho, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
For the second question: obviously not.
– kimchi lover
Jan 1 at 4:50
add a comment |
For the second question: obviously not.
– kimchi lover
Jan 1 at 4:50
For the second question: obviously not.
– kimchi lover
Jan 1 at 4:50
For the second question: obviously not.
– kimchi lover
Jan 1 at 4:50
add a comment |
1 Answer
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oldest
votes
The famous Moment problem tells you that you cannot determine the distribution function from the sequence of moments in general. It is very easy to construct different distributions with same mean and variance.
In the present case $Esum frac { |t|^{n}|X|^{n}} {n!} <infty$ for $|t| <1$ so it is legitimate to compute the generating function $Ee^{tX}$ as $sum t^{n}=frac 1 {1-t}$ for $|t| <1$.
answered Jan 1 at 5:14
Kavi Rama MurthyKavi Rama Murthy
52.4k32055
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
The famous Moment problem tells you that you cannot determine the distribution function from the sequence of moments in general. It is very easy to construct different distributions with same mean and variance.
In the present case $Esum frac { |t|^{n}|X|^{n}} {n!} <infty$ for $|t| <1$ so it is legitimate to compute the generating function $Ee^{tX}$ as $sum t^{n}=frac 1 {1-t}$ for $|t| <1$.
answered Jan 1 at 5:14
Kavi Rama MurthyKavi Rama Murthy
52.4k32055
add a comment |
The famous Moment problem tells you that you cannot determine the distribution function from the sequence of moments in general. It is very easy to construct different distributions with same mean and variance.
In the present case $Esum frac { |t|^{n}|X|^{n}} {n!} <infty$ for $|t| <1$ so it is legitimate to compute the generating function $Ee^{tX}$ as $sum t^{n}=frac 1 {1-t}$ for $|t| <1$.
answered Jan 1 at 5:14
Kavi Rama MurthyKavi Rama Murthy
52.4k32055
add a comment |
The famous Moment problem tells you that you cannot determine the distribution function from the sequence of moments in general. It is very easy to construct different distributions with same mean and variance.
In the present case $Esum frac { |t|^{n}|X|^{n}} {n!} <infty$ for $|t| <1$ so it is legitimate to compute the generating function $Ee^{tX}$ as $sum t^{n}=frac 1 {1-t}$ for $|t| <1$.
answered Jan 1 at 5:14
Kavi Rama MurthyKavi Rama Murthy
52.4k32055
The famous Moment problem tells you that you cannot determine the distribution function from the sequence of moments in general. It is very easy to construct different distributions with same mean and variance.
In the present case $Esum frac { |t|^{n}|X|^{n}} {n!} <infty$ for $|t| <1$ so it is legitimate to compute the generating function $Ee^{tX}$ as $sum t^{n}=frac 1 {1-t}$ for $|t| <1$.
answered Jan 1 at 5:14
Kavi Rama MurthyKavi Rama Murthy
52.4k32055
answered Jan 1 at 5:14
Kavi Rama MurthyKavi Rama Murthy
52.4k32055
answered Jan 1 at 5:14
Kavi Rama MurthyKavi Rama Murthy
52.4k32055
answered Jan 1 at 5:14
Kavi Rama MurthyKavi Rama Murthy
52.4k32055
52.4k32055
add a comment |
add a comment |
For the second question: obviously not.
– kimchi lover
Jan 1 at 4:50