C6 - Statistical Distributions

• A random variable is a variable whose value depends on the outcome of a random variable.
• The range of values that a random variable can take is called its sample space.
• A variable can take any of a range of specific values.
• The variable is discrete if it can only take certain numerical values.
• The variable is random if the outcome is not known until the experiment is carried out.
• A probability distribution fully describes the probability of any outcome in the sample space.
• When all probabilities are the same, the distribution is known as a discrete uniform distribution.
• The sum of the probabilities of all outcomes of an event add up to 1. For a random variable X, you can write sum of P(X=x) = 1 for all x.
• When you are carrying out a number of trials in an experiment or survey, you can define a random variable X to represent the number of successful trials.
• You can model X with a binomial distribution, B(n, p), if:

  • there are a fixed number of trials, n
  • there are two possible outcomes (success and failure)
  • there is a fixed probability of success, p
  • the trials are independent of each other
• A cumulative probability function for a random variable X tells you the sum of all the individual probabilities up to and including the given value x.