Maths Multivariate Normal Distribution question

Watch
SuprDooprPoopr
Badges: 7
Rep:
?
#1
Report Thread starter 2 months ago
#1
I'm pretty sure I can do part iii) and iv), but I'm not sure what they're actually asking me to do for the first question and second questions... can anyone let me know what I'm supposed to do for them or give me a start/clue?
Name:  2020-12-10 (4).png
Views: 9
Size:  27.6 KB
0
reply
SuprDooprPoopr
Badges: 7
Rep:
?
#2
Report Thread starter 2 months ago
#2
bump
0
reply
mqb2766
Badges: 19
Rep:
?
#3
Report 2 months ago
#3
(Original post by SuprDooprPoopr)
I'm pretty sure I can do part iii) and iv), but I'm not sure what they're actually asking me to do for the first question and second questions... can anyone let me know what I'm supposed to do for them or give me a start/clue?
Name:  2020-12-10 (4).png
Views: 9
Size:  27.6 KB
For i) what sort of distribution. Is it? Normal (mean vector, covariance matrix, ....) or ...
ii) is similar, but involves the sum of two random (normal) variables. It's a straight forward result.
Last edited by mqb2766; 2 months ago
0
reply
0le
Badges: 21
Rep:
?
#4
Report 2 months ago
#4
I have a feeling part two is related to the central limit theorem.
0
reply
mqb2766
Badges: 19
Rep:
?
#5
Report 2 months ago
#5
(Original post by 0le)
I have a feeling part two is related to the central limit theorem.
The distribution of the sum of two normal random variables is a well known result.
0
reply
SuprDooprPoopr
Badges: 7
Rep:
?
#6
Report Thread starter 2 months ago
#6
(Original post by mqb2766)
For i) what sort of distribution. Is it? Normal (mean vector, covariance matrix, ....) or ...
ii) is similar, but involves the sum of two random (normal) variables. It's a straight forward result.
for i) i put Q ~ N(100, 15^2) and E ~ N(0,5^2) because I think they're both normal distributions... but I don't know "What is the distribution of the random vector (Q,E)'?" means to be honest.
0
reply
mqb2766
Badges: 19
Rep:
?
#7
Report 2 months ago
#7
(Original post by SuprDooprPoopr)
for i) i put Q ~ N(100, 15^2) and E ~ N(0,5^2) because I think they're both normal distributions... but I don't know "What is the distribution of the random vector (Q,E)'?" means to be honest.
Both of the things you mention are univariate (single random variable) disrributions.
You want to combine them into a joint, multivariate distribution, as per the title of the thread.
You must have some notes on this?
0
reply
SuprDooprPoopr
Badges: 7
Rep:
?
#8
Report Thread starter 2 months ago
#8
(Original post by mqb2766)
Both of the things you mention are univariate (single random variable) disrributions.
You want to combine them into a joint, multivariate distribution, as per the title of the thread.
You must have some notes on this?
I've looked through all my notes, and lecture notes on the course, but I can't find anything on combining them. I don't know how to combine them...
0
reply
mqb2766
Badges: 19
Rep:
?
#9
Report 2 months ago
#9
(Original post by SuprDooprPoopr)
I've looked through all my notes, and lecture notes on the course, but I can't find anything on combining them. I don't know how to combine them...
The independent in the question may help?
Your notes will cover the form of a multivariate normal distribution, as will googling it.
You say you're ok with the conditional part iiii) but that will use the joint distribution (ii) so you must have some info about it? Describe what you understand/are confused about.
0
reply
SuprDooprPoopr
Badges: 7
Rep:
?
#10
Report Thread starter 2 months ago
#10
(Original post by mqb2766)
The independent in the question may help?
Your notes will cover the form of a multivariate normal distribution, as will googling it.
You say you're ok with the conditional part iiii) but that will use the joint distribution (ii) so you must have some info about it? Describe what you understand/are confused about.
Okay, I didn't see that last part about them being independent so I should be able to do some of it. I'm not sure about the questions because random vectors are usually just like (x1,..., xn) so I'm not sure what I'm supposed to do when its (Q,E)', plus it being transposed as well.
0
reply
mqb2766
Badges: 19
Rep:
?
#11
Report 2 months ago
#11
(Original post by SuprDooprPoopr)
Okay, I didn't see that last part about them being independent so I should be able to do some of it. I'm not sure about the questions because random vectors are usually just like (x1,..., xn) so I'm not sure what I'm supposed to do when its (Q,E)', plus it being transposed as well.
n=2
x1 = Q
x2 = E
It's as simple a multivariate normal distribution as you get.
By default, vectors are column vectors.
0
reply
SuprDooprPoopr
Badges: 7
Rep:
?
#12
Report Thread starter 2 months ago
#12
(Original post by mqb2766)
n=2
x1 = Q
x2 = E
It's as simple a multivariate normal distribution as you get.
By default, vectors are column vectors.
so a bivariate normal distribution?
0
reply
mqb2766
Badges: 19
Rep:
?
#13
Report 2 months ago
#13
(Original post by SuprDooprPoopr)
so a bivariate normal distribution?
Yes.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Which of these would you use to help with making uni decisions?

Webinars (73)
12.01%
Virtual campus tours/open days (149)
24.51%
Live streaming events (51)
8.39%
Online AMAs/guest lectures (55)
9.05%
A uni comparison tool (142)
23.36%
An in-person event when available (138)
22.7%

Watched Threads

View All
Latest
My Feed