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We need to calculate cov(X,Y)=EXY - EX*EY, var(X) and var(Y). To do it, we have to know marginal distributions of both random variables X and Y. This can be done by "integrating the other variable out" of the joint density function. I will show you how to calculate the marginal density function of X:
I know that to find the correlation coefficient of x1 x 1 and x2 x 2, it is: Px1x2 = cov(x1,x2) σ1σ2 P x 1 x 2 = c o v (x 1, x 2) σ 1 σ 2. Furthermore, I believe the σ σ can be derived from the diagonals of the covariance matrix, but I'm not sure how to find cov(x1,x2) c o v (x 1, x 2).
Then we have r = 0.8 r = 0.8. So our correlation coefficient is 0.8 0.8. But it is unclear to me what is the use of the regression equation in the above problem. The regression equation is there to tell you the direction of the correlation. If you know r2 = 0.64 r 2 = 0.64, then r = ±0.8 r = ± 0.8. To decide on whether the correlation is ...
I've been looking all over the internet and have been having trouble finding good uses of a covariance matrix to find the correlation coefficient. I know that, from a simple $2 \times2$ variance-covariance matrix, the correlation is given by $\mathrm{COR}\left(X,Y\right)=\frac{\mathrm{COV} \left(X,Y\right)}{\sqrt{Var\left(X\right)\cdot V a r ...
Let X be a Bernoulli random variable with success parameter p, where p is uniformly distributed over the interval (0,1). Suppose p is chosen, then two independent observations of X (call them X_1 and X_2) are made. What is the unconditional correlation coefficient between X_1 and X_2?
Calculate the correlation coefficient between X X and Y Y, that is: Corr(X, Y) = Cov(X, Y) σXσY Corr (X, Y) = Cov (X, Y) σ X σ Y. I am having trouble calculating the covariance since I don't know the common pdf, only the marginal ones, and since X X and Y Y are not independent, I can't figure out how to do this. Could someone help me please?
From a population consisting of the numbers: $\\lbrace 1,2 \\ldots 10 \\rbrace$, two samples are chosen from it without replacement. If the random variable denoting the first choice is X and the second
Calculate covariance $\mathbb{C}ov(X,Y)$ . Calculate correlation coefficient. Ask Question Asked 6 ...
I know that if these events are independent that the probability of them all occurring is simply P(A) ⋅ P(B) ⋅ P(C). So if the probability of each happening is 10% then all three have a 10% ⋅ 10% ⋅ 10% = 0.1% probability of occurring. But how would this formula change if the events were not independent but were instead positively ...
Computing the Correlation Coefficient of Two Random Variables. 0. Finding Conditional expectance, variance ...