|
|
| Author |
Message |
Long Nguyen
science forum beginner
Joined: 22 Jun 2006
Posts: 3
|
 Posted: Thu Jun 22, 2006 12:28 pm Post subject:
many random variable problem
|
|
|
exam tomorrow, its probably late in getting a response, lets try.
just a simple question P(2X + 3Y < 30).
E(X) = 0, VAR(X) = 4, E(Y)=10, VAR(Y)=9.
ans:0.5
can someone assist me in working this out.
--
"Hi..."
- cOS
cossmo @at gmail . com |
|
| Back to top |
|
 |
Pubkeybreaker
science forum Guru
Joined: 24 Mar 2005
Posts: 333
|
| Posted: Thu Jun 22, 2006 1:12 pm Post subject:
Re: many random variable problem
|
|
|
Long Nguyen wrote:
| Quote: | exam tomorrow, its probably late in getting a response, lets try.
just a simple question P(2X + 3Y < 30).
E(X) = 0, VAR(X) = 4, E(Y)=10, VAR(Y)=9.
ans:0.5
can someone assist me in working this out.
|
What are the pdf's for X and Y? |
|
| Back to top |
|
|
Pubkeybreaker
science forum Guru
Joined: 24 Mar 2005
Posts: 333
|
| Posted: Thu Jun 22, 2006 1:24 pm Post subject:
Re: many random variable problem
|
|
|
Long Nguyen wrote:
| Quote: | exam tomorrow, its probably late in getting a response, lets try.
just a simple question P(2X + 3Y < 30).
E(X) = 0, VAR(X) = 4, E(Y)=10, VAR(Y)=9.
ans:0.5
can someone assist me in working this out.
|
If X & Y are normally distributed the problem is trivial.
If you can't solve this problem when X & Y are normal, then
you have some serious knowledge gaps and will have great difficulty
on your exam.
We need to know how X & Y are distributed.
I assume you know how to make a change-of-variable/transformation
of a pdf? Let W = 2X + 3Y. Compute the joint pdf of X&Y,
multiply
by the Jacobian, then compute the marginal distribution of W by
integration.
Once you know the pdf for 2X + 3Y, you can compute the probability
that W < 30.
With no information about how X & Y are distributed, the problem seems
impossible. |
|
| Back to top |
|
|
Long Nguyen
science forum beginner
Joined: 22 Jun 2006
Posts: 3
|
| Posted: Fri Jun 23, 2006 1:18 am Post subject:
Re: many random variable problem
|
|
|
On 22 Jun 2006 06:24:49 -0700, "Pubkeybreaker"
<Robert_silverman@raytheon.com> wrote:
| Quote: |
Long Nguyen wrote:
exam tomorrow, its probably late in getting a response, lets try.
just a simple question P(2X + 3Y < 30).
E(X) = 0, VAR(X) = 4, E(Y)=10, VAR(Y)=9.
ans:0.5
can someone assist me in working this out.
If X & Y are normally distributed the problem is trivial.
If you can't solve this problem when X & Y are normal, then
you have some serious knowledge gaps and will have great difficulty
on your exam.
We need to know how X & Y are distributed.
I assume you know how to make a change-of-variable/transformation
of a pdf? Let W = 2X + 3Y. Compute the joint pdf of X&Y,
multiply
by the Jacobian, then compute the marginal distribution of W by
integration.
Once you know the pdf for 2X + 3Y, you can compute the probability
that W < 30.
With no information about how X & Y are distributed, the problem seems
impossible.
|
yes, there are many serious knowledge gaps, either my brain or the
teaching levels here at my uni or a combination of both.
it is assumed X & Y is normally distributed.
thanks for your reply, it has helped alot. |
|
| Back to top |
|
|
Pubkeybreaker
science forum Guru
Joined: 24 Mar 2005
Posts: 333
|
| Posted: Fri Jun 23, 2006 10:45 am Post subject:
Re: many random variable problem
|
|
|
Long Nguyen wrote:
| Quote: | On 22 Jun 2006 06:24:49 -0700, "Pubkeybreaker"
Robert_silverman@raytheon.com> wrote:
yes, there are many serious knowledge gaps, either my brain or the
teaching levels here at my uni or a combination of both.
it is assumed X & Y is normally distributed.
|
Are they *independent*?? The problem did not say.
Do you know how to find the distribution of a random variable
that is the sum of two normally distributed random variables?
| Quote: |
thanks for your reply, it has helped alot.
|
What book are you using? |
|
| Back to top |
|
|
Long Nguyen
science forum beginner
Joined: 22 Jun 2006
Posts: 3
|
| Posted: Sun Jun 25, 2006 4:15 am Post subject:
Re: many random variable problem
|
|
|
| Quote: |
yes, there are many serious knowledge gaps, either my brain or the
teaching levels here at my uni or a combination of both.
it is assumed X & Y is normally distributed.
Are they *independent*?? The problem did not say.
Do you know how to find the distribution of a random variable
that is the sum of two normally distributed random variables?
thanks for your reply, it has helped alot.
What book are you using?
|
yes, they are independant. I am not really sure what you are
asking me.
I am using devore, statistics for engineers, 2nd ed. it doesn't
have info on differences of joint distribution.
anyhow, the test went 'ok'. i was stuck on one particular question and
wasted alot of time on it. this is what I can recall.
this is a 5.4% risk of catching some type of disease. a sample of 2000
men was taken and 78 of them was diagnosed with the disease. 64 of
1500 women was diagnosed with the disease. it is said that men have
a higher risk of catching this disease, what test statistics would you
use?
--
"Hi..."
- cOS
cossmo @at gmail . com |
|
| Back to top |
|
|
Google
|
|
| Back to top |
|
|
|
|
The time now is Thu Oct 20, 2011 11:58 pm | All times are GMT
|
|
Copyright © 2004-2005 DeniX Solutions SRL
|
|
Other DeniX Solutions sites:
Electronics forum |
Medicine forum |
Unix/Linux blog |
Unix/Linux documentation |
Unix/Linux forums |
send newsletters
|
| |
|
Powered by phpBB © 2001, 2005 phpBB Group
|
|
FAQ
Search
Memberlist
Usergroups
Profile
Log in to check your private messages
Log in
Forum index
»
Science and Technology
»
Math
»
Undergraduate
