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Maths Multivariate Normal Distribution question

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?
2020-12-10 (4).png
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Reply 2
Avatar for mqb2766
mqb2766
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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?
2020-12-10 (4).png

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.
(edited 3 years ago)
Reply 3
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0le
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I have a feeling part two is related to the central limit theorem.
Reply 4
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mqb2766
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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.
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.
Reply 6
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mqb2766
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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?
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...
Reply 8
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mqb2766
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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.
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.
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.
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?
Original post by SuprDooprPoopr
so a bivariate normal distribution?

Yes.

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