Mixing
The mean value of sample moment with order k
up vote
0
down vote
favorite
I've this problem of statistics that I can't resolve. So I hope that someone can halp me.
The problem is this:
Let sampling moments $overline{X_n^k}=frac{1}{n}sum_{i=1}^nX_i^k$, where for $k=1$ $overline{X_n^k}=overline{X_n}$.
Show that $E(overline{X_n^k})=E(X)$, where $E(Y)$ is the mean value of $Y$.
I did this:
$E(overline{X_n^k})=E(frac{1}{n}sum_{i=1}^nX_i^k)=frac{1}{n}E(sum_{i=1}^nX_i^k)$
I think that for ID of $X_i$, I can write:
$frac{1}{n}E(sum_{i=1}^nX_i^k)=frac{1}{n}*nE(X_i^k)=E(X_i^k)$.
Is this correct? And how can I go on? I thought to use the moment generating functions, but I don't know use it.
Thank you for your help.
statistics means sampling
asked 21 hours ago
user502400
214
add a comment |
up vote
0
down vote
favorite
I've this problem of statistics that I can't resolve. So I hope that someone can halp me.
The problem is this:
Let sampling moments $overline{X_n^k}=frac{1}{n}sum_{i=1}^nX_i^k$, where for $k=1$ $overline{X_n^k}=overline{X_n}$.
Show that $E(overline{X_n^k})=E(X)$, where $E(Y)$ is the mean value of $Y$.
I did this:
$E(overline{X_n^k})=E(frac{1}{n}sum_{i=1}^nX_i^k)=frac{1}{n}E(sum_{i=1}^nX_i^k)$
I think that for ID of $X_i$, I can write:
$frac{1}{n}E(sum_{i=1}^nX_i^k)=frac{1}{n}*nE(X_i^k)=E(X_i^k)$.
Is this correct? And how can I go on? I thought to use the moment generating functions, but I don't know use it.
Thank you for your help.
statistics means sampling
asked 21 hours ago
user502400
214
Well, $E(overline{X^k})=E(X)$ certainly doesn't hold in general. This, if at all, can only be true for particular value distributions, so we need more information on those.
– Andreas
21 hours ago
Did you intend to say "Show that $Eleft(overline{X_n^k}right)=Eleft(X^kright)$" with a $,^k$ on the right hand side?
– Henry
16 hours ago
I think that $X_i$ have random variable generative $Xsim N(mu,sigma ^2)$. My teacher didn't specify it, for this reason I didn't write it. But before of this exercise we treated this random variable.
– user502400
44 mins ago
I don't know Henry. This is the text that my teacher gave us, but she may have been wrong.
– user502400
39 mins ago
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I've this problem of statistics that I can't resolve. So I hope that someone can halp me.
The problem is this:
Let sampling moments $overline{X_n^k}=frac{1}{n}sum_{i=1}^nX_i^k$, where for $k=1$ $overline{X_n^k}=overline{X_n}$.
Show that $E(overline{X_n^k})=E(X)$, where $E(Y)$ is the mean value of $Y$.
I did this:
$E(overline{X_n^k})=E(frac{1}{n}sum_{i=1}^nX_i^k)=frac{1}{n}E(sum_{i=1}^nX_i^k)$
I think that for ID of $X_i$, I can write:
$frac{1}{n}E(sum_{i=1}^nX_i^k)=frac{1}{n}*nE(X_i^k)=E(X_i^k)$.
Is this correct? And how can I go on? I thought to use the moment generating functions, but I don't know use it.
Thank you for your help.
statistics means sampling
asked 21 hours ago
user502400
214
I've this problem of statistics that I can't resolve. So I hope that someone can halp me.
The problem is this:
Let sampling moments $overline{X_n^k}=frac{1}{n}sum_{i=1}^nX_i^k$, where for $k=1$ $overline{X_n^k}=overline{X_n}$.
Show that $E(overline{X_n^k})=E(X)$, where $E(Y)$ is the mean value of $Y$.
I did this:
$E(overline{X_n^k})=E(frac{1}{n}sum_{i=1}^nX_i^k)=frac{1}{n}E(sum_{i=1}^nX_i^k)$
I think that for ID of $X_i$, I can write:
$frac{1}{n}E(sum_{i=1}^nX_i^k)=frac{1}{n}*nE(X_i^k)=E(X_i^k)$.
Is this correct? And how can I go on? I thought to use the moment generating functions, but I don't know use it.
Thank you for your help.
statistics means sampling
statistics means sampling
asked 21 hours ago
user502400
214
asked 21 hours ago
user502400
214
asked 21 hours ago
user502400
214
asked 21 hours ago
user502400
214
asked 21 hours ago
user502400
214
214
Well, $E(overline{X^k})=E(X)$ certainly doesn't hold in general. This, if at all, can only be true for particular value distributions, so we need more information on those.
– Andreas
21 hours ago
Did you intend to say "Show that $Eleft(overline{X_n^k}right)=Eleft(X^kright)$" with a $,^k$ on the right hand side?
– Henry
16 hours ago
I think that $X_i$ have random variable generative $Xsim N(mu,sigma ^2)$. My teacher didn't specify it, for this reason I didn't write it. But before of this exercise we treated this random variable.
– user502400
44 mins ago
I don't know Henry. This is the text that my teacher gave us, but she may have been wrong.
– user502400
39 mins ago
add a comment |
Well, $E(overline{X^k})=E(X)$ certainly doesn't hold in general. This, if at all, can only be true for particular value distributions, so we need more information on those.
– Andreas
21 hours ago
Did you intend to say "Show that $Eleft(overline{X_n^k}right)=Eleft(X^kright)$" with a $,^k$ on the right hand side?
– Henry
16 hours ago
I think that $X_i$ have random variable generative $Xsim N(mu,sigma ^2)$. My teacher didn't specify it, for this reason I didn't write it. But before of this exercise we treated this random variable.
– user502400
44 mins ago
I don't know Henry. This is the text that my teacher gave us, but she may have been wrong.
– user502400
39 mins ago
Well, $E(overline{X^k})=E(X)$ certainly doesn't hold in general. This, if at all, can only be true for particular value distributions, so we need more information on those.
– Andreas
21 hours ago
Well, $E(overline{X^k})=E(X)$ certainly doesn't hold in general. This, if at all, can only be true for particular value distributions, so we need more information on those.
– Andreas
21 hours ago
Did you intend to say "Show that $Eleft(overline{X_n^k}right)=Eleft(X^kright)$" with a $,^k$ on the right hand side?
– Henry
16 hours ago
Did you intend to say "Show that $Eleft(overline{X_n^k}right)=Eleft(X^kright)$" with a $,^k$ on the right hand side?
– Henry
16 hours ago
I think that $X_i$ have random variable generative $Xsim N(mu,sigma ^2)$. My teacher didn't specify it, for this reason I didn't write it. But before of this exercise we treated this random variable.
– user502400
44 mins ago
I think that $X_i$ have random variable generative $Xsim N(mu,sigma ^2)$. My teacher didn't specify it, for this reason I didn't write it. But before of this exercise we treated this random variable.
– user502400
44 mins ago
I don't know Henry. This is the text that my teacher gave us, but she may have been wrong.
– user502400
39 mins ago
I don't know Henry. This is the text that my teacher gave us, but she may have been wrong.
– user502400
39 mins ago
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3004811%2fthe-mean-value-of-sample-moment-with-order-k%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Well, $E(overline{X^k})=E(X)$ certainly doesn't hold in general. This, if at all, can only be true for particular value distributions, so we need more information on those.
– Andreas
21 hours ago
Did you intend to say "Show that $Eleft(overline{X_n^k}right)=Eleft(X^kright)$" with a $,^k$ on the right hand side?
– Henry
16 hours ago
I think that $X_i$ have random variable generative $Xsim N(mu,sigma ^2)$. My teacher didn't specify it, for this reason I didn't write it. But before of this exercise we treated this random variable.
– user502400
44 mins ago
I don't know Henry. This is the text that my teacher gave us, but she may have been wrong.
– user502400
39 mins ago