IGNOU MCS 66 2026 2027 - Explain the Bernoulli, Binomial, Poisson and Hypergeometric distributi

Question

Explain the Bernoulli, Binomial, Poisson and Hypergeometric distributions. Compare their assumptions,
parameters and applications.

03 Aug 2026

Answer :

Word Count : 700

Probability distributions are mathematical models used to describe the likelihood of different outcomes of a random experiment. Discrete probability distributions are applicable when the random variable takes countable values. Among the most important discrete distributions are the Bernoulli, Binomial, Poisson, and Hypergeometric distributions. Each distribution has distinct assumptions, parameters, and practical applications. The Bernoulli distribution is the simplest discrete probability distribution. It describes an experiment that has only two possible outcomes: success and failure. Let the probability of success be (p), where (0 \leq p \leq 1), and the probability of failure be (1-p). A Bernoulli random variable (X) takes the value 1 for success and 0 for failure. Its probability mass function is given by: [ P(X=x)=p^x(1-p)^{1-x}, \quad x=0,1. ] The mean of the Bernoulli distribution is (p), and the variance is (p(1-p)). It is commonly used in situations such as determining whether a student passes or fails an examination, whether a manufactured item is defective or non-defective, or whether a coin toss results in heads or tails. The Binomial distribution is an extension of the Bernoulli distribution. It represents the

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