Statistics - estimation Watch

Nilsdejongh
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#1
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A bit stuck on this question!

Consider two random variables; X1 has an expected value of 3 and a variance of 4;
X2 has an expected value of 2 and a variance of 1. X1 and X2 are correlated and the coefficient of correlation is – 0.3.

Find the expected value and variance of Y1 and Y2
where
(a)Y1 = X1 - X2
(b)Y2 = 2X1 + X2 + 4
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rayquaza17
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#2
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(Original post by Nilsdejongh)
A bit stuck on this question!

Consider two random variables; X1 has an expected value of 3 and a variance of 4;
X2 has an expected value of 2 and a variance of 1. X1 and X2 are correlated and the coefficient of correlation is – 0.3.

Find the expected value and variance of Y1 and Y2
where
(a)Y1 = X1 - X2
(b)Y2 = 2X1 + X2 + 4
So what work have you done so far?
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Nilsdejongh
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(Original post by rayquaza17)
So what work have you done so far?
I was thinking going down the route of for finding E(Y1) just substituting the E(X1) and E(X2) values into the Y1 Formula..

Eg. E(Y1) = E(x1) - E(x2)
E(Y1) = 3 - 2 = 1?

And then for the variance could i just do Var(Y1) = Var(X1) - Var(X2)
..Var(Y1) = 4-1 = 3

Not sure if this method is right however...
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rayquaza17
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(Original post by Nilsdejongh)
E(Y1) = 3 - 2 = 1?
Yes


(Original post by Nilsdejongh)
And then for the variance could i just do Var(Y1) = Var(X1) - Var(X2)
..Var(Y1) = 4-1 = 3
Not quite.
I want to post two formulas here to help you, but I don't want to write something that you haven't learned about. Could you tell me if you know what covariance is?
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Nilsdejongh
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I'm aware that the Covariance is the relationship between the 2 variables.. and then to get a more accurate overview you essentially standardise it go get the correlation coefficient?

Cov (x,y) = E(xy) - E(x)E(y)

Cor Coeff = Cov(x,y) /Var(x)Var(y)

not sure what to do with these formulas to work out Var(y1) and Var(y2)
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rayquaza17
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(Original post by Nilsdejongh)
I'm aware that the Covariance is the relationship between the 2 variables.. and then to get a more accurate overview you essentially standardise it go get the correlation coefficient?

Cov (x,y) = E(xy) - E(x)E(y)

Cor Coeff = Cov(x,y) /Var(x)Var(y)

not sure what to do with these formulas to work out Var(y1) and Var(y2)
Yes so note that:
var(ax+by)=a^{2}var(x)+b^{2}var(  y)+2abcov(x,y)

And in this case you don't explicitly know cov(x1,x2) but you do know var(x1), var(x2) and the correlation coefficient between them, so you can work it out.
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Nilsdejongh
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(Original post by rayquaza17)
Yes so note that:
var(ax+by)=a^{2}var(x)+b^{2}var(  y)+2abcov(x,y)

And in this case you don't explicitly know cov(x1,x2) but you do know var(x1), var(x2) and the correlation coefficient between them, so you can work it out.
However, with that equation you've supplied i'd put in X1 and x2 right? how would i go from having the Var(x1) Var(x2) and Cov(x1,x2) to getting the variances of y1 and y2?
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