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

PMF to CDF

Comparison Discrete RV: 1.Zero slope 2.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.

PDF of X

Example 3.3

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.

Definitions

Properties of Variance/Standard of Deviation

Discrete Example

Quiz 3.3