probability & statistics

descriptive statistics

median index is (n+1)/2

probability basics

AND and OR rule for a discrete single variable

why we multiply in tree diagrams

P(A|B) = P(A) ⇒ P(B|A) = P(B)

expected value and variance basics

E[X + Y] = E[X] + E[Y]

E[cX] = c * E[X] where c is a constant

E[XY] = E[X] * E[Y] where X and Y are independent variables

measuring the spread of data: mean absolute deviation and mean squared deviation

Var[X] = E[X²] - (E[X]²)

Var[kX] = k² * Var[X]

Var[X + Y] = Var[X] + Var[Y] where X and Y are independent variables

Var[aX + bY] = a²Var[X] + b²Var[Y] + 2ab cov(X, Y)

defining covariance

cov(X, Y) = E[XY] - E[X]E[Y]

deriving the E[X] and Var[X] for the iid variables

estimating the population variance using the sample mean and the sample size

Markov's inequality

Chebyshev's inequality

probability distribution stuff

expected value and variance of a binomial distribution

expected value and variance of a geometric distribution

expected value and variance of a geometric distribution (when success isn't included) (incomplete)

probability function of the Poisson distribution

if X is a positive continuous random variable with a memoryless property, then X is exponentially distributed

variance of an uniform distribution (incomplete)

expected value and variance of an exponential distribution

deviation and regression

sum of squared deviations computational formula

sum of products of deviations computational formula

the net residual is zero if and only if the line crosses the mean

for a fixed slope the best fit line passes through the mean

finding the gradient of the best fit line

understanding the correlation coefficient

other ways to express correlation coefficient

-1 ≤ corr(X, Y) ≤ 1

understanding the R² score