All Questions
11 questions
3
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78
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Let $X, Y$ be independent RVs given the variances and no means what is correlation coefficient of $X$ and $Z=2X+Y$?
Let $X, Y$ be independent RV given the variance and no means what is correlation coefficient of $X$ and $Z=2X+Y$?
Given $var(X)=3, var(Y)=4$ and $\mathbf{E}[X]$ and $\mathbf{E}[Y]$ are not known, let $...
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2
votes
1
answer
103
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Solving an equation to find two unknown weights given an unbiased estimate
Apologies if this is a simple question; I am reviewing out of Seber and Lee's book on regression and I am pretty rusty in my linear algebra
Suppose that $X_1, ..., X_n$ have a common mean $\mu$ and ...
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0
votes
0
answers
133
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Correlation coefficient $(Y=aX+b)$
Consider two random variables $X$ and $Y$.
Assume now that $Y=aX+b$ where $a<0$ and $-\infty<b<\infty$. Determine the value of the correlation coefficient $\rho(X,Y)$.
My attempt.
$$\rho(X,...
- 495
1
vote
1
answer
101
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Correlation.. covariance.. I am so lost
This monday I'll take my exam in Investment analyses. My teacher usually gives a matrix with covariances and beta's, which makes it easy to find Expected return/ Variance. He just posted some exam ...
0
votes
1
answer
278
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Variance of a difference variable
I have a question I'm quite struggling with.
$\newcommand{\Var}{{\rm Var}} \newcommand{\Cov}{{\rm Cov}}$
Let's say I have variable $x_1$, and I know that $x_2=x_1+d$, with $d$ being a random variable ...
- 11
2
votes
2
answers
210
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Derive the LLN for a certain sequence
I have a sequence of dependent random variables $X_1, X_2...X_n$. Each RV is correlated with two other RVs and uncorrelated with the others.The ones that are correlated satisfy the condition $Cov(X_i,...
- 21
3
votes
1
answer
3k
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Variance of Z for Z = X + Y, when X and Y correlated
So I'm trying to show that ${\rm Var}(Z) \le 2({\rm Var}(X)+{\rm Var}(Y))$ for $Z = X + Y$. This seems to be pretty easy to show given that $X$ and $Y$ are uncorrelated. But I'm running into trouble ...
- 167
2
votes
1
answer
123
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Correlation influence on two variable coefficients
Consider the linear model $Y = B_{0} + B_{1}X_{1} + B_{2}X_{2} + e$,
where the columns $X_{1}$ and $X_{2}$ of the design matrix have mean $0$ and length $1$. That is $X_{i}'X_{i} = 1$ and $X_{i}'J = 0$...
- 111
1
vote
2
answers
3k
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ANOVA determining percentage of variation
The Financial Review wished to estimate the amount of annual government spending using tax revenue and level of nationwide debt. Data from 1958-2008 (inclusive) was used. All variables were measured ...
- 13
2
votes
0
answers
94
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Finding correlation coefficient
if I have A and B with the following known variables:
with $E[A]$, $E[B]$ , $\sigma_{A}$ , $\sigma_B$
and correlation coefficient: $\rho_{AB}$ (assign numbers if you like)
Say: $C=0.6A+0.4B$
Then ...
- 21
2
votes
1
answer
196
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Do we need an unbiased estimator of the variance?
"Although it is nice to have an unbiased estimator of the variance, we do not really need it to understand the relation between our independent variable and our dependent variable. Why?"
I think I ...
- 21