poisson distribution [5]

compare and differentiate between binomial and poisson distribution

* both the binomial distribution and the poisson distribution are used to model/describe count data
* the binomial variable is the total number of successes in n trials where the trials are independent with a constant probability of success denoted by p for each of them
* the poisson distribution is the number of successes/responses in a defined time period or space where the rate per space unit or time unit is denoted by (λ)
* the binomial variable has a maximum value which is the number of trials (n), while the poisson variable, in theory, does not have that upper limit
* both binomial and poisson variables are example of

discrete variables

what is the type of graph (left skewed, right skewed or symmetric) is the poisson distribution?

mostly right-skewed except for large λ, then it becomes symmetric

if Y has a poisson distribution with average rate λ \n (that is Y \~ Poisson(λ)) then what is the:

* mean of y
* variance of y
* standard deviation of y

* λ
* λ
* √λ

how to compute poisson probabilities in excel for point and cumulative probabilities

* point probability → =POISSON.DIST (k, λ, 0)
* cumulative probability → =POISSON.DIST (k, λ, 1)