CS 3341 Lecture Notes - Lecture 16: Count Von Count, Stochastic Process, Binomial Distribution
16 May 2018
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Section 6.3 Counting Processes
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Section 6.3 Counting Processes
Ernie: You know, whenever I’m not sleepy, Bert tells me to count sheep.
Count von Count: “Count Sheep”? Who’s that?
It’s about time
A stochastic process is a random variable that depends on time.
Analyzing a stochastic process
The possible values of
There are two broad kinds of possible times, each requiring different analysis:
A counting process is a stochastic process that gives the number of items counted
by time .
Examples of questions we can answer using counting processes as models:
The probability of at most 10 messages arriving in the next 15 minutes
The probability of at least 4 customers arriving in the next hour
The probability of at least 100 hits on a website in the next day
In general, we ask about the value of the count at some time .
Section 6.3 Counting Processes
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A discrete-time option: Binomial processes
Use the Binomial distribution to count the number of “successes” after trials. The
independent “time” variable is the number of trials .
Framed
How do we relate the number of trials to real time?
Example: With a frame size of 3 seconds, how many frames is 8 minutes?
frames
Section 6.3 Counting Processes
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How do we relate frames and arrivals to a Binomial process?
Arrival rate
For the sake of illustration, use “minutes” for real time units.
Given -minute frames, compute the expected number of arrivals after minutes.
What is the average number of arrivals per minute?
