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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
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
Continuous Random Variables Chapter 5 Nutan S. Mishra Department of Mathematics and Statistics University of South Alabama.
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Use of moment generating functions. Definition Let X denote a random variable with probability density function f(x) if continuous (probability mass function.
Discrete Random Variable. Outline Expected Value (Section 2.5) Functions of a Random Variable (Section 2.6) Expected Value of a Derived Random Variable.
Review of Basic Probability and Statistics
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Probability Distributions – Finite RV’s Random variables first introduced in Expected Value def. A finite random variable is a random variable that can.
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A random variable that has the following pmf is said to be a binomial random variable with parameters n, p The Binomial random variable.
Review of Probability and Random Processes
The Erik Jonsson School of Engineering and Computer Science Chapter 2 pp William J. Pervin The University of Texas at Dallas Richardson, Texas.
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