# ENG EC 381 Lecture Notes - Lecture 6: Cumulative Distribution Function, Standard Deviation, Random Variable

## Document Summary

Discrete uniform (p) e[x] = (k + l)/2. Var{x] = (l k)(l k + 2)/12. Example: we send a bit over a wire with a voltage in volts. Map bit 0 to -1 and 1 to +1. X: signal: e[x] = x px(x) where x {--1, 1} Aside: later, we"ll the laws of laws of large numbers. These tell us that arithmetic means over repeated trials converge to the expected value as the number of trial grows. Function of random variable: a function y = g(x) of a discreet random variable x is a discreet random variable (derived random variable) Y takes values in sy (also discrete: sy = {g(x): x s, if the original mapping from outcomes s to values was x(s), then y(s) = g(x(s)) Py(y) = p [y y] = p [{x sx: g(x)}] Y = x + 3 - sx = { -1, 1} - sy = {2, 4}