Integration of a pdf, expected value

• alias

Homework Statement

Show that E[Y^4] = 3, where Y~N(0,1)

Homework Equations

E[(Y-mu)^4]/[E(Y-mu)^2]^2 = 3
E(Y^4) = 1/sprt(2pi)*intregral (y^4)*e^(-y^2/2)

The Attempt at a Solution

I have expanded and simplified the first equation above and cannot get it to equal 3. I think it's possible to solve the second using integration by parts but I can't find what to use for
[u, du, dv, v] in order to integrate by parts. Any help would be appreciated. Thanks.

Sorry, it's a definite integral in from -inf to inf.

Homework Statement

Show that E[Y^4] = 3, where Y~N(0,1)

Homework Equations

E[(Y-mu)^4]/[E(Y-mu)^2]^2 = 3
E(Y^4) = 1/sprt(2pi)*intregral (y^4)*e^(-y^2/2)

The Attempt at a Solution

I have expanded and simplified the first equation above and cannot get it to equal 3. I think it's possible to solve the second using integration by parts but I can't find what to use for
[u, du, dv, v] in order to integrate by parts. Any help would be appreciated. Thanks.

You might have to try several things until you get something that will work. What have you tried so far? Another approach that is often useful is to look at dI(a)/da or d^2I(a)/da^2, where I(a) = integral_{y=-inf..inf} exp(-a*y^2/2) dy.

RGV

I tried integration by parts but the integral I end up with makes no sense to me.

I tried integration by parts but the integral I end up with makes no sense to me.

If you show your work we have the basis of a discussion.

RGV

Just spit-balling, is there a way to use some substitutions to make this look something like the pdf of a gamma distribution? Then use what you know about that?

I integrated the Gaussian distribution, it took a long time but I finally got the right answer. After making a substitution, integration by parts worked. I would like to know if the formula: E[(Y-mu)^4]/[E(Y-mu)^2]^2, is useless for answering this question though. Thanks guys.
The text passage is a discussion from a homework help forum, where a student is asking for help with a mathematical problem related to the expected value of a normal distribution. The student provides the problem statement, relevant equations, and their attempts at a solution, and receives suggestions and feedback from others.
single_question_with_answer

the passage contains a single mathematical question: "show that e[y^4] = 3, where y~n(0,1)". the answer to this question is provided at the end of the passage, where the student states, "i integrated the gaussian distribution, it took a long time but i finally got the right answer."
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Integration of a pdf, expected value

• alias

Homework Statement

Show that E[Y^4] = 3, where Y~N(0,1)

Homework Equations

E[(Y-mu)^4]/[E(Y-mu)^2]^2 = 3
E(Y^4) = 1/sprt(2pi)*intregral (y^4)*e^(-y^2/2)

The Attempt at a Solution

I have expanded and simplified the first equation above and cannot get it to equal 3. I think it's possible to solve the second using integration by parts but I can't find what to use for
[u, du, dv, v] in order to integrate by parts. Any help would be appreciated. Thanks.

Sorry, it's a definite integral in from -inf to inf.

Homework Statement

Show that E[Y^4] = 3, where Y~N(0,1)

Homework Equations

E[(Y-mu)^4]/[E(Y-mu)^2]^2 = 3
E(Y^4) = 1/sprt(2pi)*intregral (y^4)*e^(-y^2/2)

The Attempt at a Solution

I have expanded and simplified the first equation above and cannot get it to equal 3. I think it's possible to solve the second using integration by parts but I can't find what to use for
[u, du, dv, v] in order to integrate by parts. Any help would be appreciated. Thanks.

You might have to try several things until you get something that will work. What have you tried so far? Another approach that is often useful is to look at dI(a)/da or d^2I(a)/da^2, where I(a) = integral_{y=-inf..inf} exp(-a*y^2/2) dy.

RGV

I tried integration by parts but the integral I end up with makes no sense to me.

I tried integration by parts but the integral I end up with makes no sense to me.

If you show your work we have the basis of a discussion.

RGV

Just spit-balling, is there a way to use some substitutions to make this look something like the pdf of a gamma distribution? Then use what you know about that?

I integrated the Gaussian distribution, it took a long time but I finally got the right answer. After making a substitution, integration by parts worked. I would like to know if the formula: E[(Y-mu)^4]/[E(Y-mu)^2]^2, is useless for answering this question though. Thanks guys.
user
The text passage is a discussion from a homework help forum, where a student is asking for help with a mathematical problem related to the expected value of a normal distribution. The student provides the problem statement, relevant equations, and their attempts at a solution, and receives suggestions and feedback from others.

TYPE: SINGLE_QUESTION_WITH_ANSWER

The passage contains a single mathematical question: "Show that E[Y^4] = 3, where Y~N(0,1)". The answer to this question is provided at the end of the passage, where the student states, "I integrated the Gaussian distribution, it took a long time but I finally got the right answer."