STA 309 Chapter 6: Chapter 6 Notes
Document Summary
Random variable: value is based on the outcome of a random event. Discrete random variable: can list all the outcomes. Continuous random variable: can take on any value (possibly bounded on one or both sides) Probability model: the collection of all the possible values and the probabilities associated with them. Cumulative distribution function (cdf): f(x) = p(x x) Parameter: the expected value (mean) of the probability model. Expected value: found by multiplying each possible value of the random variable by the probability that it occurs and summing all those products. Does not shift the variance or standard deviation. Multiplying each value of a random variable by a constant: Multiplies the variance by the square of the constant. Multiples standard deviation by absolute value of the constant. Additional rule for expected values of random variables: e(x y) = e(x) . Addition rule for variances of (independent) random variables: var(x y) = Var(x) + var(y) if x and y are independent.
