ECON10005 Lecture Notes - Lecture 4: Probability Distribution, Uncountable Set, Random Variable
Document Summary
Lecture 8: continuous random variables and normal distribution. Continuous random variable: a variable which has a continuum of outcomes: number of uncountably infinite, generally defined on real numbers or some interval of real numbers. Probability density function: probabilities for continuous random variables are calculated for ranges of outcomes, not individual outcomes, not p(x=x) but instead p(x1 < x x2, note: f(x) is not a probability, f(x) p(x = x) Uniform distribution: a uniform distribution is defined on an interval [a, b] Every interval of equal length has equal probability: x can take any real values, (- , , mean: e(x) = , varia(cid:374)(cid:272)e: var(cid:894)x(cid:895) = 2. The normal distribution is probably the most used distribution in probability and statistics. Finding normal distribution quantiles (percentiles: (cid:862)reverse(cid:863) pro(cid:271)le(cid:373) of fi(cid:374)di(cid:374)g pro(cid:271)a(cid:271)ilities, common problem in statistics, given probability p, find zp such that p(z > zp) = p. Look up 1 p in the normal table and find corresponding z.
