Binomial Distribution
The binomial distribution models the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, as is usually the case in research programmes, the draws are not independent. However, where the population N is much larger (at least 10 times larger) than n, the binomial distribution is a good approximation.
If the random variable X follows the binomial distribution with parameters n ∈ N and p ∈ [0,1], we write X ~ B(n, p). The probability of getting exactly k successes in n trials is given by the probability mass function (Exhibit 33.9):
$$ P(X=k) = \binom{n}{k}p^k(1-p)^{n-k} $$Where:
$$\binom{n}{k}=\frac{n!}{k!(n-k)!}$$The mean and variance of this distribution is:
$$mean,\, E(X)= \bar{p} = µ_X = np $$ $$variance,\, Var(X)=σ_X^2= np(1-p)$$Note: In Excel you may use the BINOM.DIST (k, n, p, cumulative) function to compute P(k).
Use the Search Bar to find content on MarketingMind.
Marketing Analytics Workshop
In an analytics-driven business environment, this analytics-centred consumer marketing workshop is tailored to the needs of consumer analysts, marketing researchers, brand managers, category managers and seasoned marketing and retailing professionals.
What they SHOULD TEACH at Business Schools
Is marketing education fluffy too?
Experiential Learning via Simulators | Best Way to Train Marketers
Marketing simulators impart much needed combat experiences, equipping practitioners with the skills to succeed in the consumer market battleground. They combine theory with practice, linking the classroom with the consumer marketplace.
