Let A, B, C be sets. Prove A × (B ∪ C) = (A × B) ∪ (A × C).
Let A, B, C be sets. (a, b) ∈ A × (B ∪ C) ⇐⇒ a ∈ A and b ∈ (B ∪ C), ⇐⇒ a ∈ A and (b ∈ B or b ∈ C ), ⇐⇒ (a, b) ∈ (A × B) or (a, b) ∈ (A × C), ⇐⇒ (a, b) ∈ (A × B) ∪ (A × C). Therefore, A × (B ∪ C) = (A × B) ∪ (A × C).
Heteroscedasticity occurs when the variability of a variable is unequal across the range of values of a different variable that predicts it. That is, the variance of one variable, call it x1, affects a second variable, call it x2, differently than it would affect another variable, call it x3.
When would be the appropriate time to use a z-score? What about a t-score?
T-scores are generally used for small sample sizes. When reading the problem, look for sample mean, x-bar, sample sizes less than 20, or standard deviations, s. Z-scores are generally used for large sample sizes. When reading the problem, look for the population mean, mu, sample sizes greater that 20, or the population standard deviation, sigma.