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Probability Density Function (PDF)
It is not possible to define a PMF function for a continuous variable because P[X=x]=0.We can, however, define a probability density function.
The Expected Value of a function
Derived Discrete Random Variable
Derived Continuous Random Variable
Discrete Example
Key Points
• An average is a typical value of a random variable.
• The next question:– “What are the chances of observing an
event far from the average?”• The variance of a random variable X describes
the difference between X and its expected value.