For a Poisson distribution  the mean value is 

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UGC NET Paper 2: Commerce 4th March 2023 Shift 2
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  1. 2
  2. 5
  3. 10
  4. 25

Answer (Detailed Solution Below)

Option 2 : 5
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UGC NET Paper 1: Held on 21st August 2024 Shift 1
50 Qs. 100 Marks 60 Mins

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Key Points

  • Poisson distribution:
    •  The Poisson distribution is a discrete probability function that means the variable can only take specific values in a given list of numbers, probably infinite. A Poisson distribution measures how many times an event is likely to occur within “x” period of time. 
    • A Poisson experiment is a statistical experiment that classifies the experiment into two categories, such as success or failure. Poisson distribution is a limiting process of the binomial distribution.

    • A Poisson random variable “x” defines the number of successes in the experiment. This distribution occurs when there are events that do not occur as the outcomes of a definite number of outcomes. Poisson distribution is used under certain conditions. They are:

    • The number of trials “n” tends to infinity
    • Probability of success “p” tends to zero
    • np = 1 is finite
    • The formula for the Poisson distribution function is given by:

      f(x) =(e– λ λx)/x!

      Where,

      e is the base of the logarithm

      x is a Poisson random variable

      λ is an average rate of value

    • For the Poisson distribution, λ is always greater than 0. For Poisson distribution, the mean and the variance of the distribution are equal.

    • Here  λ=5.Therefore mean is also equal to 5

​Hence the correct answer is 5.

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