It is fairly easy to derive the mean and variance of the binomial distribution because we can depict Bernoulli trials in several ways.
Actually, a Poisson distribution is not described by events with two possible outcomes and a constant probability of success as are Bernoulli trials. However, under certain conditions, we can use the Poisson distribution to solve Bernoulli problems.
When we have Bernoulli trials and want to calculate the probability of r successes in n trials where n is large, sometimes we use the normal approximation to the binomial distribution.
Binomial pdf The probability density function that comes from Bernoulli trials
. Blocks Account for some systematic source of variability within the data and remove it from the experimental error by placing it within the blocks, such as selecting fields as blocks in a variety trial experiment because they have different soil types.