Expected Value of Beta Distribution [closed]
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What is the expected value of 1/(1+X) with X ~ Beta(2,3)?
probability statistics probability-distributions
edited Nov 20 at 18:35
Jean Marie
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asked Nov 20 at 18:31
karsonlauch
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closed as off-topic by StubbornAtom, Davide Giraudo, KReiser, user10354138, Cesareo Nov 21 at 2:10
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – StubbornAtom, Davide Giraudo, KReiser, user10354138, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
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down vote
favorite
What is the expected value of 1/(1+X) with X ~ Beta(2,3)?
probability statistics probability-distributions
edited Nov 20 at 18:35
Jean Marie
28.2k41848
asked Nov 20 at 18:31
karsonlauch
1
closed as off-topic by StubbornAtom, Davide Giraudo, KReiser, user10354138, Cesareo Nov 21 at 2:10
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – StubbornAtom, Davide Giraudo, KReiser, user10354138, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
1
There is a straightforward method: find the pdf or cdf of R.V. $Y=phi(X)$ with $phi(x)=1/(1+x)$. I imagine you have already done this kind of exercise...
– Jean Marie
Nov 20 at 18:38
What I find funny is that WolframAlpha understands the exact same question that you posted: wolframalpha.com/input/…
– Federico
Nov 21 at 16:01
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
What is the expected value of 1/(1+X) with X ~ Beta(2,3)?
probability statistics probability-distributions
edited Nov 20 at 18:35
Jean Marie
28.2k41848
asked Nov 20 at 18:31
karsonlauch
1
What is the expected value of 1/(1+X) with X ~ Beta(2,3)?
probability statistics probability-distributions
probability statistics probability-distributions
edited Nov 20 at 18:35
Jean Marie
28.2k41848
asked Nov 20 at 18:31
karsonlauch
1
edited Nov 20 at 18:35
Jean Marie
28.2k41848
asked Nov 20 at 18:31
karsonlauch
1
edited Nov 20 at 18:35
Jean Marie
28.2k41848
edited Nov 20 at 18:35
Jean Marie
28.2k41848
edited Nov 20 at 18:35
Jean Marie
28.2k41848
28.2k41848
asked Nov 20 at 18:31
karsonlauch
1
asked Nov 20 at 18:31
karsonlauch
1
asked Nov 20 at 18:31
karsonlauch
1
1
closed as off-topic by StubbornAtom, Davide Giraudo, KReiser, user10354138, Cesareo Nov 21 at 2:10
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – StubbornAtom, Davide Giraudo, KReiser, user10354138, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by StubbornAtom, Davide Giraudo, KReiser, user10354138, Cesareo Nov 21 at 2:10
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – StubbornAtom, Davide Giraudo, KReiser, user10354138, Cesareo
If this question can be reworded to fit the rules in the help center, please edit the question.
1
There is a straightforward method: find the pdf or cdf of R.V. $Y=phi(X)$ with $phi(x)=1/(1+x)$. I imagine you have already done this kind of exercise...
– Jean Marie
Nov 20 at 18:38
What I find funny is that WolframAlpha understands the exact same question that you posted: wolframalpha.com/input/…
– Federico
Nov 21 at 16:01
add a comment |
1
There is a straightforward method: find the pdf or cdf of R.V. $Y=phi(X)$ with $phi(x)=1/(1+x)$. I imagine you have already done this kind of exercise...
– Jean Marie
Nov 20 at 18:38
What I find funny is that WolframAlpha understands the exact same question that you posted: wolframalpha.com/input/…
– Federico
Nov 21 at 16:01
1
1
There is a straightforward method: find the pdf or cdf of R.V. $Y=phi(X)$ with $phi(x)=1/(1+x)$. I imagine you have already done this kind of exercise...
– Jean Marie
Nov 20 at 18:38
There is a straightforward method: find the pdf or cdf of R.V. $Y=phi(X)$ with $phi(x)=1/(1+x)$. I imagine you have already done this kind of exercise...
– Jean Marie
Nov 20 at 18:38
What I find funny is that WolframAlpha understands the exact same question that you posted: wolframalpha.com/input/…
– Federico
Nov 21 at 16:01
What I find funny is that WolframAlpha understands the exact same question that you posted: wolframalpha.com/input/…
– Federico
Nov 21 at 16:01
add a comment |
1 Answer
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The PDF of $X$ is $12x(1-x)^2$. You have to compute
$$
12int_0^1 frac1{1+x}x(1-x)^2dx = 12int_0^1left(4-3x+x^2-frac4{1+x}right)dx = 34 - 48 log(2) .
$$
answered Nov 20 at 18:39
Federico
2,910511
why the PDF of X is 12x(1-x)^2?
– karsonlauch
Nov 21 at 4:14
@karsonlauch By definition: en.wikipedia.org/wiki/…
– Federico
Nov 21 at 15:54
You can easily check that $int_0^1 x^{2-1} (1-x)^{3-1} , dx = frac1{12}$.
– Federico
Nov 21 at 15:57
Or you can use $B(2,3)=frac{Gamma(2)Gamma(3)}{Gamma(2+3)}=frac{1!2!}{4!}=frac1{12}$.
– Federico
Nov 21 at 15:58
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
The PDF of $X$ is $12x(1-x)^2$. You have to compute
$$
12int_0^1 frac1{1+x}x(1-x)^2dx = 12int_0^1left(4-3x+x^2-frac4{1+x}right)dx = 34 - 48 log(2) .
$$
answered Nov 20 at 18:39
Federico
2,910511
why the PDF of X is 12x(1-x)^2?
– karsonlauch
Nov 21 at 4:14
@karsonlauch By definition: en.wikipedia.org/wiki/…
– Federico
Nov 21 at 15:54
You can easily check that $int_0^1 x^{2-1} (1-x)^{3-1} , dx = frac1{12}$.
– Federico
Nov 21 at 15:57
Or you can use $B(2,3)=frac{Gamma(2)Gamma(3)}{Gamma(2+3)}=frac{1!2!}{4!}=frac1{12}$.
– Federico
Nov 21 at 15:58
add a comment |
up vote
1
down vote
The PDF of $X$ is $12x(1-x)^2$. You have to compute
$$
12int_0^1 frac1{1+x}x(1-x)^2dx = 12int_0^1left(4-3x+x^2-frac4{1+x}right)dx = 34 - 48 log(2) .
$$
answered Nov 20 at 18:39
Federico
2,910511
why the PDF of X is 12x(1-x)^2?
– karsonlauch
Nov 21 at 4:14
@karsonlauch By definition: en.wikipedia.org/wiki/…
– Federico
Nov 21 at 15:54
You can easily check that $int_0^1 x^{2-1} (1-x)^{3-1} , dx = frac1{12}$.
– Federico
Nov 21 at 15:57
Or you can use $B(2,3)=frac{Gamma(2)Gamma(3)}{Gamma(2+3)}=frac{1!2!}{4!}=frac1{12}$.
– Federico
Nov 21 at 15:58
add a comment |
up vote
1
down vote
up vote
1
down vote
The PDF of $X$ is $12x(1-x)^2$. You have to compute
$$
12int_0^1 frac1{1+x}x(1-x)^2dx = 12int_0^1left(4-3x+x^2-frac4{1+x}right)dx = 34 - 48 log(2) .
$$
answered Nov 20 at 18:39
Federico
2,910511
The PDF of $X$ is $12x(1-x)^2$. You have to compute
$$
12int_0^1 frac1{1+x}x(1-x)^2dx = 12int_0^1left(4-3x+x^2-frac4{1+x}right)dx = 34 - 48 log(2) .
$$
answered Nov 20 at 18:39
Federico
2,910511
answered Nov 20 at 18:39
Federico
2,910511
answered Nov 20 at 18:39
Federico
2,910511
answered Nov 20 at 18:39
Federico
2,910511
2,910511
why the PDF of X is 12x(1-x)^2?
– karsonlauch
Nov 21 at 4:14
@karsonlauch By definition: en.wikipedia.org/wiki/…
– Federico
Nov 21 at 15:54
You can easily check that $int_0^1 x^{2-1} (1-x)^{3-1} , dx = frac1{12}$.
– Federico
Nov 21 at 15:57
Or you can use $B(2,3)=frac{Gamma(2)Gamma(3)}{Gamma(2+3)}=frac{1!2!}{4!}=frac1{12}$.
– Federico
Nov 21 at 15:58
add a comment |
why the PDF of X is 12x(1-x)^2?
– karsonlauch
Nov 21 at 4:14
@karsonlauch By definition: en.wikipedia.org/wiki/…
– Federico
Nov 21 at 15:54
You can easily check that $int_0^1 x^{2-1} (1-x)^{3-1} , dx = frac1{12}$.
– Federico
Nov 21 at 15:57
Or you can use $B(2,3)=frac{Gamma(2)Gamma(3)}{Gamma(2+3)}=frac{1!2!}{4!}=frac1{12}$.
– Federico
Nov 21 at 15:58
why the PDF of X is 12x(1-x)^2?
– karsonlauch
Nov 21 at 4:14
why the PDF of X is 12x(1-x)^2?
– karsonlauch
Nov 21 at 4:14
@karsonlauch By definition: en.wikipedia.org/wiki/…
– Federico
Nov 21 at 15:54
@karsonlauch By definition: en.wikipedia.org/wiki/…
– Federico
Nov 21 at 15:54
You can easily check that $int_0^1 x^{2-1} (1-x)^{3-1} , dx = frac1{12}$.
– Federico
Nov 21 at 15:57
You can easily check that $int_0^1 x^{2-1} (1-x)^{3-1} , dx = frac1{12}$.
– Federico
Nov 21 at 15:57
Or you can use $B(2,3)=frac{Gamma(2)Gamma(3)}{Gamma(2+3)}=frac{1!2!}{4!}=frac1{12}$.
– Federico
Nov 21 at 15:58
Or you can use $B(2,3)=frac{Gamma(2)Gamma(3)}{Gamma(2+3)}=frac{1!2!}{4!}=frac1{12}$.
– Federico
Nov 21 at 15:58
add a comment |
1
There is a straightforward method: find the pdf or cdf of R.V. $Y=phi(X)$ with $phi(x)=1/(1+x)$. I imagine you have already done this kind of exercise...
– Jean Marie
Nov 20 at 18:38
What I find funny is that WolframAlpha understands the exact same question that you posted: wolframalpha.com/input/…
– Federico
Nov 21 at 16:01