Probability from convolution of generating function
up vote
0
down vote
favorite
I have to calulate two probabilities from convolution of generating function,
$P(X_1+X_2...+X_n = k)$
$P(X_1+X_2...+X_n > k)$
Where $X_i in (1,2...m)$(probability is 1/m)
how should i start it in case when we have digits i would make something like this:
$(sum_{i=0}^{9}x_i)^n$
and then take argument before x^k and divide it by n^10.
probability combinatorics
asked Nov 21 at 21:21
Gokuruto
83
add a comment |
up vote
0
down vote
favorite
I have to calulate two probabilities from convolution of generating function,
$P(X_1+X_2...+X_n = k)$
$P(X_1+X_2...+X_n > k)$
Where $X_i in (1,2...m)$(probability is 1/m)
how should i start it in case when we have digits i would make something like this:
$(sum_{i=0}^{9}x_i)^n$
and then take argument before x^k and divide it by n^10.
probability combinatorics
asked Nov 21 at 21:21
Gokuruto
83
$f_{X+Y} = f_X ast f_Y$ and $F_{X+Y} = f_{X+Y} ast theta = f_X ast f_Y ast theta$ where $theta(x) = 1$ for $x ge 0$ and $f_X$ is the pdf of $X$
– reuns
Nov 21 at 21:40
So $f_x = 1/m$ when x>0 and 0 o.w. and f_y would look the same then i need to make convolution of it and this will be solution ?
– Gokuruto
Nov 21 at 21:53
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have to calulate two probabilities from convolution of generating function,
$P(X_1+X_2...+X_n = k)$
$P(X_1+X_2...+X_n > k)$
Where $X_i in (1,2...m)$(probability is 1/m)
how should i start it in case when we have digits i would make something like this:
$(sum_{i=0}^{9}x_i)^n$
and then take argument before x^k and divide it by n^10.
probability combinatorics
asked Nov 21 at 21:21
Gokuruto
83
I have to calulate two probabilities from convolution of generating function,
$P(X_1+X_2...+X_n = k)$
$P(X_1+X_2...+X_n > k)$
Where $X_i in (1,2...m)$(probability is 1/m)
how should i start it in case when we have digits i would make something like this:
$(sum_{i=0}^{9}x_i)^n$
and then take argument before x^k and divide it by n^10.
probability combinatorics
probability combinatorics
asked Nov 21 at 21:21
Gokuruto
83
asked Nov 21 at 21:21
Gokuruto
83
asked Nov 21 at 21:21
Gokuruto
83
asked Nov 21 at 21:21
Gokuruto
83
asked Nov 21 at 21:21
Gokuruto
83
83
$f_{X+Y} = f_X ast f_Y$ and $F_{X+Y} = f_{X+Y} ast theta = f_X ast f_Y ast theta$ where $theta(x) = 1$ for $x ge 0$ and $f_X$ is the pdf of $X$
– reuns
Nov 21 at 21:40
So $f_x = 1/m$ when x>0 and 0 o.w. and f_y would look the same then i need to make convolution of it and this will be solution ?
– Gokuruto
Nov 21 at 21:53
add a comment |
$f_{X+Y} = f_X ast f_Y$ and $F_{X+Y} = f_{X+Y} ast theta = f_X ast f_Y ast theta$ where $theta(x) = 1$ for $x ge 0$ and $f_X$ is the pdf of $X$
– reuns
Nov 21 at 21:40
So $f_x = 1/m$ when x>0 and 0 o.w. and f_y would look the same then i need to make convolution of it and this will be solution ?
– Gokuruto
Nov 21 at 21:53
$f_{X+Y} = f_X ast f_Y$ and $F_{X+Y} = f_{X+Y} ast theta = f_X ast f_Y ast theta$ where $theta(x) = 1$ for $x ge 0$ and $f_X$ is the pdf of $X$
– reuns
Nov 21 at 21:40
$f_{X+Y} = f_X ast f_Y$ and $F_{X+Y} = f_{X+Y} ast theta = f_X ast f_Y ast theta$ where $theta(x) = 1$ for $x ge 0$ and $f_X$ is the pdf of $X$
– reuns
Nov 21 at 21:40
So $f_x = 1/m$ when x>0 and 0 o.w. and f_y would look the same then i need to make convolution of it and this will be solution ?
– Gokuruto
Nov 21 at 21:53
So $f_x = 1/m$ when x>0 and 0 o.w. and f_y would look the same then i need to make convolution of it and this will be solution ?
– Gokuruto
Nov 21 at 21:53
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
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%2f3008385%2fprobability-from-convolution-of-generating-function%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
$f_{X+Y} = f_X ast f_Y$ and $F_{X+Y} = f_{X+Y} ast theta = f_X ast f_Y ast theta$ where $theta(x) = 1$ for $x ge 0$ and $f_X$ is the pdf of $X$
– reuns
Nov 21 at 21:40
So $f_x = 1/m$ when x>0 and 0 o.w. and f_y would look the same then i need to make convolution of it and this will be solution ?
– Gokuruto
Nov 21 at 21:53