C3) Correlation vs Covariance

A1) Mutually Exclusive vs Independent Events

A2) Conditional Probability Formula for Independent Events

A3) Law of Large Numbers (LLN)

A4) If you test positive for cancer, what is the probability that you in fact has cancer?

A5) Are Disjoint Events Independent?

B1) What is a Random Variable?

B2) Expected Value of a Random Variable

B3) Random Variable: Variance and Standard Deviation

B4) Prove that E(cX) = cE(X)

B5) Prove that Var(cX)=ccVar(X)

B6) Var(X)=E(X^2)-[E(X)]^2

B7) Bernoulli Random Variable

C1) Random Variables: Mean and Standard Deviation

C2) Covariance vs Variance

C3) Correlation vs Covariance

C4) Cov(X,Y)=E(XY)-E(X)E(Y)

C5) If X and Y are independent, then Cov(X,Y)=0

C6) Var(X+Y)=Var(X)+Var(Y)+2Cov(X,Y)

D1) Standard Normal Distribution

D2) What is z-score?

D3) What means independent and identically distributed (iid)?

D4) Central Limit Theorem (CLT)

E1) Population Parameter vs Sample Statistic

E2) Standard Error of the Mean

E3) Random Sample

E4) Unbiased Estimator

F1) 95% Confidence Interval for Proportion (p)

F2) Normal vs Student’s t-distribution

F3) Confidence Interval for a Population Mean

F4) Margin of Error

G1) Null vs Alternative Hypothesis

G2) Type I vs Type II Errors

G3) Z-test for a Proportion

G4) T-test for the Mean

H1) Randomized Experiment

H2) Two-Sample t-Test in Python

H3) Two-Sample z-Test in Python

[luisealcock]

Why is the covariance also denoted by sigma in the last part of the formula?

[djhass]

why use covariance when correlation can tell you the direction and strengh of a relationship in a standardized/comparable form? What does covariance give us that correlation does not?

[mahaaulakh]

What would be an example of positive covariance?

[aaronpopyk]

Correlation definitely provides more intuition than covariance. It's easy to see the relationship of two variables on a scale from -1 to 1.

[hashwi]

So I understand the covariance tells us the relationship between returns on two assets. I'm just confused because if the covariance is negative that means they move inversely but what does that mean for the return.

[farahkaddoura]

So if it were a constant, the correlation would be undefined since variance would be 0 and its in the denominator?

[mitchellcarter]

Would this be the alpha or beta when talking about how a stock moves relative to the market?

[saisravanisure]

So if the correlation is 1, can we say that the variables are in a perfect linear relationship with a positive slope? Can we write Y as a linear function of X?

[danielamoreno]

so a negative correlation means that the variables are moving in opposite directions, so what does a negative or positive covariance mean?