Multinomial Distribution Vs Binomial Distribution. Out of those probability distributions binomial distribution and normal distribution are two of the most commonly occurring ones in the real life. In probability theory the multinomial distribution is a generalization of the binomial distribution for example it models the probability of counts for each side of a k sided die rolled n times.
Suppose p x 1 θ. Multinoulli distribution whereas the binomial distribution generalises the bernoulli distribution across the number of trials the multinoulli distribution generalises it across the number of outcomes that is rolling a dice instead of tossing a coin. 2 bernoullis and binomials let x 0 1 be a binary random variable e g a coin toss.
Since a poisson binomial distributed variable is a sum of n independent bernoulli distributed variables its mean and variance will simply be sums of the mean and variance of the n bernoulli distributions.
We will use a binomial distribution. Each observation falls into one of two categories. The sampling plan that lies behind data collection can take on many different characteristics and affect the optimal model for the data. Since a poisson binomial distributed variable is a sum of n independent bernoulli distributed variables its mean and variance will simply be sums of the mean and variance of the n bernoulli distributions.
