Find the Covariance of X and YCov(X,Y)=E[XY]-E[X]E[Y]Find the expection of single variables. I'm having troubles evaluation&nbsp;E[XY]. Can it be&nbsp;X·E[Y]?&nbsp;SmokerNon-SmokerTotalHeart Attack0.030.030.06No Heart Attack0.440.500.94Totals0.470.53&nbsp;

Key to "Find the Covariance of X and YCov(X,Y)=E[XY]-E[X]E[Y]Find the..."

Liesehf

Answered question

2021-11-20

Find the Covariance of X and Y

$C o v (X, Y) = E [X Y] - E [X] E [Y]$

Find the expection of single variables. I'm having troubles evaluation $E [X Y]$ . Can it be $X \cdot E [Y]$ ?

$\begin{matrix} Smoker & Non-Smoker & Total \\ Heart Attack & 0.03 & 0.03 & 0.06 \\ No Heart Attack & 0.44 & 0.50 & 0.94 \\ Totals & 0.47 & 0.53 \end{matrix}$

Answer & Explanation

Mespirst

Beginner2021-11-21Added 17 answers

Nope,

X \cdot E (Y)

is not avalid option. That is a random variable while E(XY) is a constant.
What we can say is that:

E (X Y) = E (X E (Y ∣ X))

But we really do need to know what the joint distribution is to say more (or at least a marginal and conditional distribution).

E (X Y) = \int \int_{R^{2}} x y f_{X, Y} (x, y) d x d y = \sum_{x} \sum_{y} x y P (X = x, Y = y)

E ((X E (Y ∣ X)) = \int_{R} x f_{X} (x) \int_{R} y f_{Y ∣ X = x} (y) d y d x = \sum_{y} P (X = x) \sum_{y} y P (Y = y ∣ X = x)

And so forth.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school statistics

Didn't find what you were looking for?