Question

What is poisson distribution? Explain the characteristics and formulae for poisson distribution

Answer 1

Answer:

Poisson distributions are used to calculate the probability of an event occurring over a certain interval. The interval can be one of time, area, volume or distance. You can find the probability of an event occurring is found using the formula in the Poisson distribution formula image.

⇒ It is uni-parametric in nature. As we can see, only one parameter λ is sufficient to define the distribution.

⇒ The mean of  X∼P(λ) is equal to λ.

⇒ The variance of X∼P(λ) is also equal to λ. The standard deviation, therefore, is equal to +√λ.

⇒ Depending on the value of the parameter λ, it may be unimodal or bimodal.

Answer 2

When we compress a material it tends to expand in other directions perpendicular to the direction of compression. This effect is called poisson effect.

Poisson’s ratio is the measure of the poisson effect.

Poisson Ratio =
$\frac{fraction \: of \: expansion}{fraction \: of \: comprasion}$


And if the material is stretched than it tends to contract in the transverse direction of stretching.