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# Multivariate Normal distribution

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1. https://www0.maths.ox.ac.uk/system/f.../24/sheet6.pdf

Question 5i).

So basically i have no idea how to start off. I tried calculating the probability density for X = (X1, X2)T , but the numbers do not work out nicely at all.

I have also found that E(Y) = 0 and Var(Y) = 172 (as 4*25 + 9*16 - 3*2*12), but don't know what to do with this.

pls help xx

Gregorius
2. (Original post by Gome44)
https://www0.maths.ox.ac.uk/system/f.../24/sheet6.pdf

Question 5i).

So basically i have no idea how to start off. I tried calculating the probability density for X = (X1, X2)T , but the numbers do not work out nicely at all.

I have also found that E(Y) = 0 and Var(Y) = 172 (as 4*25 + 9*16 - 3*2*12), but don't know what to do with this.

pls help xx

Gregorius
The big theorem here that helps you out is that if and are normally distributed, then so is . All you need to find out is the mean and the variance of Y and that uniquely specifies the distribution of Y.

You've found the mean of Y, but your calculation of the variance of Y is a bit off. Remember that

which gives you much nicer numbers!
3. (Original post by Gregorius)
The big theorem here that helps you out is that if and are normally distributed, then so is . All you need to find out is the mean and the variance of Y and that uniquely specifies the distribution of Y.

You've found the mean of Y, but your calculation of the variance of Y is a bit off. Remember that

which gives you much nicer numbers!
Argh i forgot the 2. Thanks
4. (Original post by Gome44)
Argh i forgot the 2. Thanks
It always happens that way...

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