STATZIKI

Input

What is the average value of the sample?

x-value

Formulas and Output

\[p(y) = \frac{\lambda^{y}e^{-\lambda}}{y!} = \frac{ 7^{ 3 } e^{- 7 }}{ 3 !} = 0.0521\] \[p(y < 3 ) = 1 - p(y \geq 3) = 1 - 0.9704 = 0.0296\] \[p(y \leq 3) = 1 - p(y > 3) = 1 - 0.9182 = 0.0818\] \[p(y > 3) = 1 - p(y \leq 3) = 1 - 0.0818 = 0.9182\] \[p(y \geq 3) = 1 - p(y < 3) = 1 - 0.0296 = 0.9704\] \[E(Y) = \lambda\ = 7\] \[V(Y) = \lambda = 7\]

Probability Distribution - Poisson

When do you use the poisson distribution?

If you have the mean λ of an event happening per unit and you are asked to find the probability of x events happening in a given time, then the poisson distribution should be used.

If the mean λ > 5 it can be approximated using the normal distribution,
where the variance = mean λ.

Example, Customer arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour, During a given hour, what are the probabilities that:
- exactly 3 costumers arriving?
- less than 3 costumers arriving?
- more than 3 costumers arriving?
- 3 or less costumers arriving?
- 3 or more costumers arriving?