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

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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

Python for Econometrics

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Silly one, is E(XY) = E(X)E(Y)? Just don’t understand E(XY).. If X is the 10 years returns of stock X, and Y is the 10 years returns of stock Y, so what does E(XY) mean? Thanks

jayz

Covariance is affected when the random variables are multiplied by a constant like Cov(aX, bY)= ab*Cov(X, Y) but they are not affected when the random variables are added to a constant like Cov(X+a, Y+b) = Cov(X, Y). Am I right?

saisravanisure

Amazing explanation! Thank you for making is so simple for us to understand.

RealTonyStock

I'm a bit about the point made at the end, why is only the important information in E(XY)?

jaclyndorey

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

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

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

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F4) Margin of Error

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

B2) Expected Value of a Random Variable

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A1) Mutually Exclusive vs Independent Events

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