11.4 Continuous Distributions

In this section we learn (i) Continuous random variable (ii) Probability density function (iii) Distribution function (Cumulative distribution function). (iv) To determine distribution function from probability density function. (v) To determine probability density function from distribution function. Sometimes a measurement such as current in a copper wire or length of lifetime of an electric bulb, can assume any value in an interval of real numbers.

Then any precision in the measurement is possible. The random variable that represents this measurement is said to be a continuous random variable. The range of the random variable includes all values in an interval of real numbers; that is, the range can be thought of as a continuum of real numbers . .

The definition of continuous random variable Definition . (Continuous Random Variable) Let S be a sample space and let a random variable X S