STATS 425 Lecture Notes - Lecture 4: Probability Distribution, Random Variable, Normal Distribution
Document Summary
Continuous rvs can take any value in an interval. Used to model physical characteristics such as time, length, position. A continuous variable has infinite precision, so p(x=x) = 0 for any x. X is a continuous random variable if there is a function f(x) so that for any constants a and b in between infinity and infinity: p(a<=x<=b) = integral from a to b of f(x) dx. For any a: p(x=a) = p(a<=x<=a) = 0. A discrete random variable does not have a density function, since if a is a possible value of a discrete rv x, we have p(x=a)>0. Random variables can be partly continuous and partly discrete. The integral from negative infinity to infinity of f(x) dx = 1. The cdf of a continuous rv is defined exactly the same as for discrete rvs: f(x) = p(x<=x) = p(x in (-infinity, x], df/dx = f(x)
