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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 (x1, x2, x3, ...xn) 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: x-axis specifies values, y-axis specifies number of occurrences
• Cumulative probability curve: x-axis specifies values, y-axis specifies the probability that the variable value X is at most a, that is Pr(X<=a)