Radiation Oncology/Medical Statistics/Variables

Random Variables
 Quantity that theoretically may assume a wide variety of actual values, even though at any given time we only observe a single value
 Probability distribution of the variable is both the specification of all values the variable can take on, as well as the frequency with which it occurs in the entire population
 A set of values observed (x_{1}, x_{2}, x_{3}, ...x_{n}) is called a sample from the population (the population being defined by the probability distribution)
 A random sample assumes that the characteristics of the sample reflects those of the entire population, of which the sample may be only a small part
 Two types of random variables:
 Discrete random variable: it is possible to identify all values that a variable may take. Example: gender
 Continuous random variable: variable may take on any value (typically within a range), and the value is only limited by the precision of the measurements. Example: height
 Probability distribution is often illustrated with a histogram:
 Probability curve: xaxis specifies values, yaxis specifies number of occurrences
 Cumulative probability curve: xaxis specifies values, yaxis specifies the probability that the variable value X is at most a, that is Pr(X<=a)