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The Poisson distribution

The Poisson distribution. for x = 0, 1, 2, 3, . . . . ., . Example. The number of particles emitted per second by a random radioactive source has a Poisson distribution with  = 4. Calculate probability of : P(X = 0), P(X = 1) and P(X = 3). = 0.0183. = 0.0733. = 0.195.

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The Poisson distribution

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  1. The Poisson distribution for x = 0, 1, 2, 3, . . . . ., Example The number of particles emitted per second by a random radioactive source has a Poisson distribution with  = 4. Calculate probability of : P(X = 0), P(X = 1) and P(X = 3) = 0.0183 = 0.0733 = 0.195

  2. The number telephone calls received at an exchange during a weekday morning follows a Poisson distribution with a mean of 4 calls per five minute period. Find the probability that: (a) there are no calls in the next five minutes (b) 3 calls are received in the next five minutes (c) fewer than 2 calls are received between 12:00 and 12:05 (d) more than 2 calls are received between 16:30 and 16:35 (a) = 0.00674 (b) = 0.0719 (c) = 0.0337 = 0.912 (d)

  3. The number of accidents per week at a certain road intersection has a Poisson distribution with parameter 2.5. Find the probability that: (a) exactly 5 accidents will occur in a week (b) less than 4 accidents will occur in 2 weeks. (a) X  Po(2.5) = 0.0668 (b) X  Po(5) 0.2650 From tables

  4. The number of letters a man receives each day has a Poisson distribution with mean 3. Find the probabilities that: (a) In one day he receives 4 letters. (b) In two days he receives less than 5 letters. (a) X  Po(3) = 0.1680 (b) X  Po(6) From tables 0.2851

  5. The number of meteorites which fall on a field in a year has a Poisson distribution with mean 3. Find the probabilities that: (a) 2 meteorites fall in a year (b) No meteorites fall in 6 months (c) More than 10 meteorites fall in three years. (a) X  Po(3) = 0.2240 (b) X  Po(1.5) e- 1.5 = 0.2231 (c) X  Po(9) 1 – P(X  10) = 0.2940

  6. A car hire company has three limousines available each day for hire. The demand for these cars follows a Poisson distribution with mean 1. Find the probabilities that: (a) The company cannot meet the demand for limousines on any one day. (b) The company cannot meet the demand for limousines on exactly one day in a five-day working week. (a) X  Po(1) P(X > 3) = 1 – P(X  3) = 0.0190 (b) Binomial: p = 0.019, q = 0.981, n = 5, x = 1 0.0880

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