Expectation of $x^n$ when $x$~$U[0,1]$ [closed]
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I'm trying to follow along with my textbook on Auction Theory, but don't understand one of the steps. I don't see how they got $E[x^N] = 1/(N+1)$ in the final step. Please see the linked image below. Any help is greatly appreciated, thanks so much!
Image here
probability probability-theory probability-distributions expected-value auction-theory
edited Dec 14 '18 at 0:40
Key Flex
8,00261233
asked Dec 14 '18 at 0:25
chillzchillz
262
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closed as off-topic by Cesareo, José Carlos Santos, amWhy, Dirk, user10354138 Dec 14 '18 at 20:24
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." – Cesareo, José Carlos Santos, amWhy, Dirk, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
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$begingroup$
I'm trying to follow along with my textbook on Auction Theory, but don't understand one of the steps. I don't see how they got $E[x^N] = 1/(N+1)$ in the final step. Please see the linked image below. Any help is greatly appreciated, thanks so much!
Image here
probability probability-theory probability-distributions expected-value auction-theory
edited Dec 14 '18 at 0:40
Key Flex
8,00261233
asked Dec 14 '18 at 0:25
chillzchillz
262
$endgroup$
closed as off-topic by Cesareo, José Carlos Santos, amWhy, Dirk, user10354138 Dec 14 '18 at 20:24
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." – Cesareo, José Carlos Santos, amWhy, Dirk, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
I'm trying to follow along with my textbook on Auction Theory, but don't understand one of the steps. I don't see how they got $E[x^N] = 1/(N+1)$ in the final step. Please see the linked image below. Any help is greatly appreciated, thanks so much!
Image here
probability probability-theory probability-distributions expected-value auction-theory
edited Dec 14 '18 at 0:40
Key Flex
8,00261233
asked Dec 14 '18 at 0:25
chillzchillz
262
$endgroup$
I'm trying to follow along with my textbook on Auction Theory, but don't understand one of the steps. I don't see how they got $E[x^N] = 1/(N+1)$ in the final step. Please see the linked image below. Any help is greatly appreciated, thanks so much!
Image here
probability probability-theory probability-distributions expected-value auction-theory
probability probability-theory probability-distributions expected-value auction-theory
edited Dec 14 '18 at 0:40
Key Flex
8,00261233
asked Dec 14 '18 at 0:25
chillzchillz
262
edited Dec 14 '18 at 0:40
Key Flex
8,00261233
asked Dec 14 '18 at 0:25
chillzchillz
262
edited Dec 14 '18 at 0:40
Key Flex
8,00261233
edited Dec 14 '18 at 0:40
Key Flex
8,00261233
edited Dec 14 '18 at 0:40
Key Flex
8,00261233
8,00261233
asked Dec 14 '18 at 0:25
chillzchillz
262
asked Dec 14 '18 at 0:25
chillzchillz
262
asked Dec 14 '18 at 0:25
chillzchillz
262
262
closed as off-topic by Cesareo, José Carlos Santos, amWhy, Dirk, user10354138 Dec 14 '18 at 20:24
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." – Cesareo, José Carlos Santos, amWhy, Dirk, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Cesareo, José Carlos Santos, amWhy, Dirk, user10354138 Dec 14 '18 at 20:24
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." – Cesareo, José Carlos Santos, amWhy, Dirk, user10354138
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
add a comment |
1 Answer
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votes
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Note:
$$E(X^n)=int_0^1 t^n dt$$
answered Dec 14 '18 at 0:34
user626255user626255
211
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add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Note:
$$E(X^n)=int_0^1 t^n dt$$
answered Dec 14 '18 at 0:34
user626255user626255
211
$endgroup$
add a comment |
$begingroup$
Note:
$$E(X^n)=int_0^1 t^n dt$$
answered Dec 14 '18 at 0:34
user626255user626255
211
$endgroup$
add a comment |
$begingroup$
Note:
$$E(X^n)=int_0^1 t^n dt$$
answered Dec 14 '18 at 0:34
user626255user626255
211
$endgroup$
Note:
$$E(X^n)=int_0^1 t^n dt$$
answered Dec 14 '18 at 0:34
user626255user626255
211
answered Dec 14 '18 at 0:34
user626255user626255
211
answered Dec 14 '18 at 0:34
user626255user626255
211
answered Dec 14 '18 at 0:34
user626255user626255
211
211
add a comment |
add a comment |
