The binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. Such a success/failure experiment is also called a Bernoulli experiment or Bernoulli trial. A simple example is: roll a standard die ten times and count the number of sixes. The distribution of this random number is a binomial distribution with n = 10 and p = 1/6.

The Poisson distribution is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate and independently of the time since the last event. The distribution was discovered by Siméon-Denis Poisson (1781-1840) and published, together with his probability theory, in 1838.

A continuous random variable describes a mathematical model of a system that can be in various states, with ranges of states having a certain probability.

Both the uniform (or rectangular) and normal distributions are common examples of continuous distributions, where the variable can take all real values withing a certain range.

Hypothesis testing is concerned with the DISTRIBUTION of a STATISTIC. You know that in real world problems, measurements such as people's heights or the number of heads in 100 coin tosses, are random variables. Often we cannot know all the measurements in a population but take a smaller SAMPLE. The important concept here is that a STATISTIC (such as the mean, median or standard deviation) of a sample is a RANDOM VARIABLE too.