PROBABILITY DENSITY FUNCTIONS (PDF)
And Continuous Random Variables
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- So far we have focused on discrete(-valued) random variables, e.g. must be an integer.
- Examples of discrete random variables:
- The number of arrivals in one second.
- The number of attempts until success.
- A continuous-valued random variable takes on a range of real values, e.g. ranges from 0 to as s varies.
- Examples of continuous(-valued) random variables:
- The time when a particular arrival occurs.
- The time between consecutive arrivals.
- A discrete random variable has a "staircase" CDF.
- A continuous random variable has (some) continuous slopes to its CDF.
- Thus, for a continuous random variable X, we can define its probability density function (pdf) by
- Note that since is non-decreasing in x, we have
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