For a Poisson distribution \(\rm P(x)=\frac{e^{-5}(5)^2}{2!}\) the mean value is 

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.