Continuous Distributions

Some measurements — the current in a wire, the lifetime of a bulb — can take any value in an interval of real numbers, to any precision. The random variable representing such a measurement is a continuous random variable; its range is a continuum, not a countable list.

This section develops the continuous parallel of §11.3's five ideas: the continuous random variable itself, its probability density function (pdf, replacing the pmf), its distribution function (cdf, defined exactly as before but now via an integral instead of a sum), and the two-way conversion betw …