Probability and statistical inference
Chapter 80 of 16 strong
RESTS ONCalculate finite independent-sum distributions, events and momentsFOUNDATIONSApply E(aX + b) = aE(X) + b and the expectation-of-a-sum rule E(X + Y) = E(X) + E(Y), preserving signs and not scaling the constant by aFOUNDATIONSApply Var(aX + b) = a^2·Var(X) and SD(aX + b) = |a|·SD(X), so the constant b does not affect spread and the sign of a is irrelevantFOUNDATIONSCalculate z = (x − mean) / standard deviation, retain its sign, and interpret its magnitude and direction as a distance from the mean in standard-deviation unitsFOUNDATIONSConstruct direct, contrapositive and contradiction arguments with justified stepsCH 1Calculate and distinguish empirical and exact sample-mean distributionsFOUNDATIONSImplement, validate and report a random simulation with justified trial and state rulesFOUNDATIONSGiven a probability statement about Z (less-than, greater-than, central or two-tail), convert it to the required less-than area and find the corresponding z quantile, exactly for the empirical-rule probability levels and by an authorised inverse-normal enclosure for other levelsFOUNDATIONSCalculate an exact conditional probability as the intersection probability divided by the conditioning-event probability, with a nonzero conditioning eventFOUNDATIONS
Linear combinations of random variables
Distribution of sample means
Confidence intervals for population means
Hypothesis tests for population means