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STATISTIC & INFORMATION THEORY (CSNB134)

STATISTIC & INFORMATION THEORY (CSNB134). MODULE 7B PROBABILITY DISTRIBUTIONS FOR RANDOM VARIABLES ( POISSON DISTRIBUTION). Overview. In Module 7, we will learn three types of distributions for random variables, which are: - Binomial distribution - Module 7A

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STATISTIC & INFORMATION THEORY (CSNB134)

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  1. STATISTIC & INFORMATION THEORY (CSNB134) MODULE 7B PROBABILITY DISTRIBUTIONS FOR RANDOM VARIABLES ( POISSON DISTRIBUTION)

  2. Overview • In Module 7, we will learn three types of distributions for random variables, which are: - Binomial distribution - Module 7A - Poisson distribution - Module 7B - Normal distribution - Module 7C • This is a Sub-Module 7B, which includes lecture slides on Poisson Distribution.

  3. The Poisson Random Variable • The Poisson random variable xis a model for data that represent the number of occurrences of a specified event in a given unit of time or space. • Examples: • The number of calls received by a switchboard during a given period of time. • The number of machine breakdowns in a day • The number of traffic accidents at a given intersection during a given time period.

  4. For values of k = 0, 1, 2, … The mean and standard deviation of the Poisson random variable are Mean: m Standard deviation: The Poisson Probability Distribution • x is the number of events that occur in a period of time or space during which an average of m such events can be expected to occur. The probability of k occurrences of this event is

  5. Exercise 1 The average number of traffic accidents on a certain section of highway is two per week. Find the probability of exactly one accident during a one-week period.

  6. Cumulative Probability Tables • You can use the cumulative probability tables to find probabilities for selected Poisson distributions. • Find the column for the correct value of m. • The row marked “k” gives the cumulative probability, P(x  k) = P(x = 0) +…+ P(x = k)

  7. Exercise 2 (Similar case of Exercise 1). What is the probability that there is exactly 1 accident? • Find the column for the correct value of m.

  8. Exercise 2 (cont.) (Similar case of Exercise 1).What is the probability that there is exactly 1 accident? P(x = 1) = P(x 1) – P(x  0) = .406 - .135 = .271 Check from formula: P(x = 1) = .2707

  9. Exercise 2 (cont.) What is the probability that 8 or more accidents happen? Is it common for an accident to happen 8 or more times in a week? P(x 8) = 1 - P(x< 8) = 1 – P(x  7) = 1 - .999 = .001 This would be very unusual (small probability) since x = 8 lies standard deviations above the mean.

  10. STATISTIC & INFORMATION THEORY (CSNB134) PROBABILITY DISTRIBUTIONS OF RANDOM VARIABLES (POISSON DISTRIBUTIONS) --END--

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