Calculate $E(X^2)$ with X uniformly distributed on [-1,2] [closed]
$begingroup$
X is uniformly distributed on $[-1,2]$.
Hence the density function should be $frac13$ and E(X) = $0.5$.
Now I want to calculate $E[X²]$. But to do that I need the density function of $X²$.
This density function should be $0$ except between $0$ and $4$.
Is $E[X²]$ uniformly distributed on $[0,4]$?
statistics probability-distributions uniform-distribution
edited Dec 18 '18 at 14:28
idea
2,15041025
asked Dec 18 '18 at 14:25
Luca9984Luca9984
11
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closed as off-topic by Did, Lord_Farin, amWhy, Dando18, Tianlalu Dec 21 '18 at 18:53
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." – Did, Lord_Farin, amWhy, Dando18, Tianlalu
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
X is uniformly distributed on $[-1,2]$.
Hence the density function should be $frac13$ and E(X) = $0.5$.
Now I want to calculate $E[X²]$. But to do that I need the density function of $X²$.
This density function should be $0$ except between $0$ and $4$.
Is $E[X²]$ uniformly distributed on $[0,4]$?
statistics probability-distributions uniform-distribution
edited Dec 18 '18 at 14:28
idea
2,15041025
asked Dec 18 '18 at 14:25
Luca9984Luca9984
11
$endgroup$
closed as off-topic by Did, Lord_Farin, amWhy, Dando18, Tianlalu Dec 21 '18 at 18:53
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." – Did, Lord_Farin, amWhy, Dando18, Tianlalu
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
"But to do that I need the density function of X²" No, your notes should explain that, for every $g$, $$E(g(X))=int_mathbb Rg(x)f_X(x)dx$$
$endgroup$
– Did
Dec 18 '18 at 14:28
$begingroup$
@Did Why are you answering in a comment?
$endgroup$
– Arthur
Dec 18 '18 at 14:38
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@Arthur Because remarks which suffice to answer the question and amount to "Please open your textbook", are not answers to me.
$endgroup$
– Did
Dec 18 '18 at 14:40
$begingroup$
@Did But they are to the unanswered queue.
$endgroup$
– Arthur
Dec 18 '18 at 14:43
$begingroup$
@Arthur I guess there are several ways to make a question exit the unanswered queue...
$endgroup$
– Did
Dec 18 '18 at 14:44
add a comment |
$begingroup$
X is uniformly distributed on $[-1,2]$.
Hence the density function should be $frac13$ and E(X) = $0.5$.
Now I want to calculate $E[X²]$. But to do that I need the density function of $X²$.
This density function should be $0$ except between $0$ and $4$.
Is $E[X²]$ uniformly distributed on $[0,4]$?
statistics probability-distributions uniform-distribution
edited Dec 18 '18 at 14:28
idea
2,15041025
asked Dec 18 '18 at 14:25
Luca9984Luca9984
11
$endgroup$
X is uniformly distributed on $[-1,2]$.
Hence the density function should be $frac13$ and E(X) = $0.5$.
Now I want to calculate $E[X²]$. But to do that I need the density function of $X²$.
This density function should be $0$ except between $0$ and $4$.
Is $E[X²]$ uniformly distributed on $[0,4]$?
statistics probability-distributions uniform-distribution
statistics probability-distributions uniform-distribution
edited Dec 18 '18 at 14:28
idea
2,15041025
asked Dec 18 '18 at 14:25
Luca9984Luca9984
11
edited Dec 18 '18 at 14:28
idea
2,15041025
asked Dec 18 '18 at 14:25
Luca9984Luca9984
11
edited Dec 18 '18 at 14:28
idea
2,15041025
edited Dec 18 '18 at 14:28
idea
2,15041025
edited Dec 18 '18 at 14:28
idea
2,15041025
2,15041025
asked Dec 18 '18 at 14:25
Luca9984Luca9984
11
asked Dec 18 '18 at 14:25
Luca9984Luca9984
11
asked Dec 18 '18 at 14:25
Luca9984Luca9984
11
11
closed as off-topic by Did, Lord_Farin, amWhy, Dando18, Tianlalu Dec 21 '18 at 18:53
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." – Did, Lord_Farin, amWhy, Dando18, Tianlalu
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Did, Lord_Farin, amWhy, Dando18, Tianlalu Dec 21 '18 at 18:53
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." – Did, Lord_Farin, amWhy, Dando18, Tianlalu
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
"But to do that I need the density function of X²" No, your notes should explain that, for every $g$, $$E(g(X))=int_mathbb Rg(x)f_X(x)dx$$
$endgroup$
– Did
Dec 18 '18 at 14:28
$begingroup$
@Did Why are you answering in a comment?
$endgroup$
– Arthur
Dec 18 '18 at 14:38
$begingroup$
@Arthur Because remarks which suffice to answer the question and amount to "Please open your textbook", are not answers to me.
$endgroup$
– Did
Dec 18 '18 at 14:40
$begingroup$
@Did But they are to the unanswered queue.
$endgroup$
– Arthur
Dec 18 '18 at 14:43
$begingroup$
@Arthur I guess there are several ways to make a question exit the unanswered queue...
$endgroup$
– Did
Dec 18 '18 at 14:44
add a comment |
$begingroup$
"But to do that I need the density function of X²" No, your notes should explain that, for every $g$, $$E(g(X))=int_mathbb Rg(x)f_X(x)dx$$
$endgroup$
– Did
Dec 18 '18 at 14:28
$begingroup$
@Did Why are you answering in a comment?
$endgroup$
– Arthur
Dec 18 '18 at 14:38
$begingroup$
@Arthur Because remarks which suffice to answer the question and amount to "Please open your textbook", are not answers to me.
$endgroup$
– Did
Dec 18 '18 at 14:40
$begingroup$
@Did But they are to the unanswered queue.
$endgroup$
– Arthur
Dec 18 '18 at 14:43
$begingroup$
@Arthur I guess there are several ways to make a question exit the unanswered queue...
$endgroup$
– Did
Dec 18 '18 at 14:44
$begingroup$
"But to do that I need the density function of X²" No, your notes should explain that, for every $g$, $$E(g(X))=int_mathbb Rg(x)f_X(x)dx$$
$endgroup$
– Did
Dec 18 '18 at 14:28
$begingroup$
"But to do that I need the density function of X²" No, your notes should explain that, for every $g$, $$E(g(X))=int_mathbb Rg(x)f_X(x)dx$$
$endgroup$
– Did
Dec 18 '18 at 14:28
$begingroup$
@Did Why are you answering in a comment?
$endgroup$
– Arthur
Dec 18 '18 at 14:38
$begingroup$
@Did Why are you answering in a comment?
$endgroup$
– Arthur
Dec 18 '18 at 14:38
$begingroup$
@Arthur Because remarks which suffice to answer the question and amount to "Please open your textbook", are not answers to me.
$endgroup$
– Did
Dec 18 '18 at 14:40
$begingroup$
@Arthur Because remarks which suffice to answer the question and amount to "Please open your textbook", are not answers to me.
$endgroup$
– Did
Dec 18 '18 at 14:40
$begingroup$
@Did But they are to the unanswered queue.
$endgroup$
– Arthur
Dec 18 '18 at 14:43
$begingroup$
@Did But they are to the unanswered queue.
$endgroup$
– Arthur
Dec 18 '18 at 14:43
$begingroup$
@Arthur I guess there are several ways to make a question exit the unanswered queue...
$endgroup$
– Did
Dec 18 '18 at 14:44
$begingroup$
@Arthur I guess there are several ways to make a question exit the unanswered queue...
$endgroup$
– Did
Dec 18 '18 at 14:44
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Guide:
You do not need the densitfy function of $X^2$. Suppose $f$ is the densify function of $X$.
To compute the expected value of $g(X)$, you can compute $int_{-1}^2 g(x) f(x) , dx$.
We just have to compute $int_{-1}^2 x^2 f(x) , dx$.
Also, $X^2$ is not uniformly distributed.
answered Dec 18 '18 at 14:28
Siong Thye GohSiong Thye Goh
100k1466117
$endgroup$
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Guide:
You do not need the densitfy function of $X^2$. Suppose $f$ is the densify function of $X$.
To compute the expected value of $g(X)$, you can compute $int_{-1}^2 g(x) f(x) , dx$.
We just have to compute $int_{-1}^2 x^2 f(x) , dx$.
Also, $X^2$ is not uniformly distributed.
answered Dec 18 '18 at 14:28
Siong Thye GohSiong Thye Goh
100k1466117
$endgroup$
add a comment |
$begingroup$
Guide:
You do not need the densitfy function of $X^2$. Suppose $f$ is the densify function of $X$.
To compute the expected value of $g(X)$, you can compute $int_{-1}^2 g(x) f(x) , dx$.
We just have to compute $int_{-1}^2 x^2 f(x) , dx$.
Also, $X^2$ is not uniformly distributed.
answered Dec 18 '18 at 14:28
Siong Thye GohSiong Thye Goh
100k1466117
$endgroup$
add a comment |
$begingroup$
Guide:
You do not need the densitfy function of $X^2$. Suppose $f$ is the densify function of $X$.
To compute the expected value of $g(X)$, you can compute $int_{-1}^2 g(x) f(x) , dx$.
We just have to compute $int_{-1}^2 x^2 f(x) , dx$.
Also, $X^2$ is not uniformly distributed.
answered Dec 18 '18 at 14:28
Siong Thye GohSiong Thye Goh
100k1466117
$endgroup$
Guide:
You do not need the densitfy function of $X^2$. Suppose $f$ is the densify function of $X$.
To compute the expected value of $g(X)$, you can compute $int_{-1}^2 g(x) f(x) , dx$.
We just have to compute $int_{-1}^2 x^2 f(x) , dx$.
Also, $X^2$ is not uniformly distributed.
answered Dec 18 '18 at 14:28
Siong Thye GohSiong Thye Goh
100k1466117
answered Dec 18 '18 at 14:28
Siong Thye GohSiong Thye Goh
100k1466117
answered Dec 18 '18 at 14:28
Siong Thye GohSiong Thye Goh
100k1466117
answered Dec 18 '18 at 14:28
Siong Thye GohSiong Thye Goh
100k1466117
100k1466117
add a comment |
add a comment |
$begingroup$
"But to do that I need the density function of X²" No, your notes should explain that, for every $g$, $$E(g(X))=int_mathbb Rg(x)f_X(x)dx$$
$endgroup$
– Did
Dec 18 '18 at 14:28
$begingroup$
@Did Why are you answering in a comment?
$endgroup$
– Arthur
Dec 18 '18 at 14:38
$begingroup$
@Arthur Because remarks which suffice to answer the question and amount to "Please open your textbook", are not answers to me.
$endgroup$
– Did
Dec 18 '18 at 14:40
$begingroup$
@Did But they are to the unanswered queue.
$endgroup$
– Arthur
Dec 18 '18 at 14:43
$begingroup$
@Arthur I guess there are several ways to make a question exit the unanswered queue...
$endgroup$
– Did
Dec 18 '18 at 14:44