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- A Random variable is a real-valued function defined on a sample space
*In words:*Some measurable aspect of a random experiment.- Types of random variables:
- discrete
- takes on a finite number of values
- Example: number of students who fail a class
- continuous
- takes on a continuous number of values
- Example: high temperature today in Kingston
- dummy or categorical
- a discrete random variable that indicates non-numerical random outcomes
- Example: 0=male student,1=female student

- Note: Functions of r.v. are themselves r.v.
For example, if Z = ln Y and Y is a random variable, then Z is also a random variable

is defined as F(x) = P(X < = x)- Cumulative Distribution Function (cdf) for a random variable X
- probability that X takes on a value < = to x

- Some Properties of CDF
- F(- ) = 0 (X can't be equal to -
- F(+ ) = 1 (X has to take on some value)
- if x > y then F(x) >= F(y) (the cdf is a non-decreasing function in its argument)

- Probability or Density function for a r.v. is defined as f(x) = dF(x)/dx [for continuous] and f(x) = P(X=x) [for discrete]
- Conditional Probability (cumulative and density)
- F(x | A ) = Prob(X<=x | A)
- f(x | A ) = dProb( X<=x | A)
- Population Parameter is any numerical value or vector of numerical values associated with the distribution of a random variable.
- Population Parameters we are often
interested in:

mean, variance, median, standard deviation, etc.

Document Last revised: 1997/1/5