Continuous Random Variable (1)
Discrete Random Variables
• Probability Mass Function (PMF)
Continuous Random Variable
P[X=x]=0
Not possible to define a PMF for a continuous random variable
Discrete Random Variables
• Cumulative Distribution Function
Comparison
Discrete RV:1. Zero slope2. Jumps in CDF
Continuous RV:A continuous function
Slope of CDF function
The slope at any point x indicates the probability that X is near x.
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.
Expected Value
Discrete Random Variable
Example
Find the expected stoppint point of the pointer
The Expected Value of a function
Derived Discrete Random Variable
Derived Continuous Random Variable
Discrete Example
Variance and Standard Deviation
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.
Properties of Variance/Standard of Deviation