week6 - Poisson Processes Model for times of occurrences...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
week 6 1 Poisson Processes Model for times of occurrences (“arrivals”) of rare phenomena where λ – average number of arrivals per time period. X – number of arrivals in a time period. •I n t time periods, average number of arrivals is λ t . How long do I have to wait until the first arrival? Let Y = waiting time for the first arrival (a continuous r.v.) then we have Therefore, which is the exponential cdf. The waiting time for the first occurrence of an event when the number of events follows a Poisson distribution is exponentially distributed.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
week 6 2 Expectation In the long run, rolling a die repeatedly what average result do you expact? In 6,000,000 rolls expect about 1,000,000 1’s, 1,000,000 2’s etc. Average is For a random variable X , the Expectation (or expected value or mean) of X is the expected average value of X in the long run. Symbols: μ , μ X , E ( X ) and EX .
Background image of page 2
week 6 3 Expectation of discrete random variable For a discrete random variable X with pmf whenever the sum converge absolutely .
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/22/2010 for the course STATISTICS STA257 taught by Professor Mcdunnough during the Fall '10 term at University of Toronto- Toronto.

Page1 / 16

week6 - Poisson Processes Model for times of occurrences...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online