Introduction to Probability · free preview

Covariance, Correlation and Two-Variable LOTUS

LOTUS in two variables, covariance as the signed co-movement measure, correlation as its unitless standardization, and what correlation does and does not encode.

1. Two-variable LOTUS

Two-variable LOTUS

2. Covariance

Covariance

3. Correlation

Correlation

4. Correlation applications and sample versions

Correlation applications and sample versions

5. Zero correlation's meaning

X and Y have correlation exactly 0. Which conclusion is justified?

6. Variance of a difference

Var(X) = 5, Var(Y) = 3, Cov(X, Y) = 1. What is Var(X - Y)?

7. Computing a covariance

E(X) = 2, E(Y) = 3, and E(XY) = 7. What is Cov(X, Y)? Enter an integer.

8. Correlation from pieces

Cov(X, Y) = 4, Var(X) = 4, Var(Y) = 16. What is the correlation? Enter a decimal like 0.5.

9. Portfolio variance

Two assets each have variance 1 with correlation -0.5. A half-half portfolio has variance (1 + rho) over 2. Enter that decimal, like 0.25.

10. In your own words

In your own words, state the most important definition, theorem or method of this lesson and explain what it says.

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