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

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

[chloechong]

Thank you so much ! I was stuck at a "coefficient of skewness" problem and your video provided valuable insights for me to solve the problem. Also your video is wonderful in explaining the theory of variance. Totally made sense to me.

[HenrikMyrhaug]

Very quick and easy to follow. Thank you!

[lauran]

This video does a very good job of explaining the math behind this step by step. I was wondering if there is another way to prove that these equations are equal, or if this is the only way? Thanks!

[GBNAssam]

Why 2E(X).E(X) is not inthe last line ....plz reply

[danielamoreno]

I am having trouble understanding why we did not apply the expected value to E(X)^2 in the 4th line of the calculation. I know you mentioned something about it being a constant but could you explain it a little more? and if it is a constant why are we not applying it? Thanks!

[iNTERnazionaleNotizia]

Are you from Japanese origin? Because you have Portuguese name 'Vitor'...and Japanese name 'Kamada'...

[alookabhai]

Plz give me the solution of e^x+2=e^x+e^2