FM - Statistics Flashcards
Discrete Random Variable - E(x)
Σxᵢpᵢ
Mean, expected value
Discrete Random Variable - Var(x)
E(x²) - E(x)²
Variance, σ²
Discrete Random Variable - Combinations of 2 < terms
E(ax + b) = aE(x) + b
Var(ax + b) = a²Var(x)
Discrete Random Variable - Combinations of 2 < variables
E(ax + by) = aE(x) + bE(y)
if x & y are independent:
E(xy) = E(x)E(y)
Var(ax±by) = a²Var(x) + b²Var(y)
Continuous Random Variable - E(x)
ₐ∫ᵇ xf(x) dx
Mean, expected value
Remember only the first x is changed by the variable in E(X)
Continuous Random Variable - Var(x)
E(x²) - E(x)²
Variance, σ²
Continuous Random Variable - Cumulative Distribution
₀∫ˣ f(x) dx = F₁(x) + … + Fₙ(n)
where Fₙ(x), a < x < n
etc
Poisson Characteristics
Random
Independent
Constant rate
Poisson Equation
P(X = r) = (e^-λ x λ^r) / (r!)
λ = E(x) = Var(x)
Binomial Characteristics
Two outcomes
Independent
Constant probability
Median From Cumulative Frequency
Median = m, where F(m) = 0.5
Least Squares Regression Line Equation
y = a + bx
b = Sₓᵧ / Sₓₓ
a = ȳ - bx̄
Spearman Rank Correlation Coefficient
rₛ = 1 - (6Σd²) / n(n²-1)
Spearman Corellation Coefficient
r = Sₓᵧ / √(SₓₓSᵧᵧ)
Chi-Squared Statistic - p-value
Probability that results produced will be at least as extreme as in the sample.
(Think about binomial or poisson)
Chi-Squared Statistic - Degrees of Freedom
(w-1)(h-1) - 1 for however many estimated values (like p)
Chi-Squared Statistic - Pooling
If the expected frequency is less than 5, the categories must be pooled.
Chi-Squared Statistic - Hypotheses
H0 : [Model] is an appropriate model for the dataset
H1: [Model] is NOT an appropriate model for the dataset
Chi-Squared Statistic - Goodness of Fit or Chi-Squared Test
Goodness of Fit gets its expected values from the distribution that is being checked. Uses chi-squared statistic (if chi-squared is more than critical value, reject h0)
Chi-Squared Test gets its expected values from the totals and stuff. Uses p-value.
Exponential Distribution
Purpose of Statistical Models
To forecast results from a set of data, to describe a real world situation
PMCC Correlation
Strong, weak
Positive, negative
