AP STATISTICS ALL FORMULAS CH 1-6 FINAL REVIEW (IN PROGRESS/INCOMPLETE)

Formula for Independent (and)

P(A and B) = P(A)*P(B)

Formula for dependent (and)

P(A and B) = P(A)*P(B|A)

Formula for dependent and independent (or)

P(A or B) = P(A) + P(B) - P(A and B)

Formula for mutually exclusive events (or)

P(A or B) = P(A) + P(B)

Formula for mutually exclusive events (and)

P(A and B)=0

Formula for independent and dependent (given)

P(A|B) = P(A and B)​/P(B)

Formula for at least 1

P(at least one) = 1-P(none)

Formula for none
(ex getting zero heads in 3 flips)

P(none) = (odds of getting none) ^ (amount of trials/objects) (P(none) = (1/2)³)

Formula for determining if the events are independent

P(B|A) = P(B)

P(A and B) = P(A) * P(B)

Mean (Expected Value)

(mu = E(X))

Discrete Variable (Mean)

mu = sum x,P(X=x)

Discrete Variable (Variance/SD)

sigma^2 = sum (x-mu)^2 P(X=x)

Standard Deviation (Random Variables)

sigma = sqrt{sigma^2}

Mean of X +- Y

mu(x) +- mu(y)

Variance of X +- Y

sqrt{(sigma(x)²) + (sigma(y)²)}

z-score (norm distribution)

x - mu / sigma

reverse z score

mu + z(sigma)

continuous random variable (PDF)

P(a < X < b) = ∫ab​ f(x) dx

continuous random variable (CDF)

f(x) = P(X<= x)

Binomial Distribution (Probability)

P(X = x) = (n x)p^x(1-p)^n-x

Binomial Distribution (Mean)

mu = np

Binomial Distribution (Variance/SD)

sigma = sqrt{np(1-p)}

Binomial Coefficient

(n x) = n! / x!(n-x)!

Geometric Distribution (Probability)

P(X = x) = (1-p)^x-1p

Geometric Distribution (Mean)

mu = 1/p

Geometric Distribution (Variance/SD)

sigma = sqrt{1-p} / p

Sampling Distributions and Standard Error

SE(xbar) = sigma/sqrt{n}

The 10% condition

n <= .10N

Slope (b) - correlations, residuals

b = r(Sy/Sx)

Intercept (a) - correlations, residuals

a = ybar - b(xbar)

Standard Deviation of the residuals (SE)

SE = sqrt{sum(yi - yhati)²/n-2} OR SE= Sy sqrt{1-r²}

IQR

Q3-Q1

TEST FOR UPPER OUTLIER

max > Q3 + 1.5(IQR)

TEST FOR LOWER OUTLIER

min < Q1 - 1.5(IQR)