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Binomial Distribution Vs. Poisson Distribution

Binomial Distribution Vs. Poisson Distribution. Binomial Distribution Used to model the number of successes (i.e. the occurrence of an event) in a finite trials ( n trials) Each trial results in one of two possible outcomes (success or failure)

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Binomial Distribution Vs. Poisson Distribution

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  1. Binomial Distribution Vs. Poisson Distribution • Binomial Distribution • Used to model the number of successes (i.e. the occurrence of an event) in a finite trials (n trials) • Each trial results in one of two possible outcomes (success or failure) • Each trial has the same probability of success, p • Independent trials • Two parameters (n, p) • Poisson Distribution • Used to model the rates of occurrence of an event, that is, the number of occurrences in a unit of measure • Events can happen at any point along a continuum • At any particular point, the probability of an event is small • The average number of events is constant over a unit of measure • Independent events • One parameter (m: the average number of events in a unit of measure )

  2. Binomial Distribution Vs. Poisson Distribution • Poisson Distribution as an Approximation of Binomial Distribution • n is very large • p is very small • m≈ n*p

  3. Problem 9.35 • A factory manager must decide whether to stock a particular spare part. Stocking the part costs $10 per day in storage and cost of capital. If the part is in stock, a broken machine can be repaired immediately. But if the part is not in stock, it takes one day to get the part from the distributor, during which time the broken machine sits idle. The cost of idling one machine for a day is $65. There are 50 machines in the plant that require this particular part. The probability that any one of them will break and require the part to be replaced on any one day is only 0.004, regardless of how long since the part was previously replaced. The machines break down independently of one another. • If you want to use a probability distribution for the number of machines that break down on a given day, would you use the Binomial or Poisson distribution? Why? • Whichever theoretical distribution you chose in part a, what are the appropriate parameters? That is, if you chose Binomial, what are the values for p and n? If you chose Poisson, what is the value for m?

  4. X = # of machines that break down on a given day • Reasons for using Binomial distribution: 1) The number of machines that break down at any point can be between 0 and 50; 2) all machines have the same probability of breaking down; 3) machines seem to break down independently of each other • Reasons for using Poisson distribution: 1) The probability of breaking down is very small; 2)Breaking down can happen at any time during the day; 3) machines seem to break down independently of each other • If we use the Binomial distribution, then n=50, p=0.004 • If we use the Poisson distribution, then m=50*0.004=0.2

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