Discussion of Applied Probability Problems from handout

What's the difference between events that are independent and disjoint (mutually exclusive)?

Random Variables

A discrete random variable X is a random variable which takes on a finite number of values, say x1, x2, …, xk.  P(X=xi) = pi, for i = 1, 2, …, k and the pi must satisfy:

  1. pi is in the interval [0, 1] for each i and
  2. p1 + p2 + … + pk = 1.

A continuous random variable X can take on all values in an interval of real numbers.  The probability of an event A, P(A), is equal to the area above A and under a probability density curve.  A probability density curve is a function f(x) that satisfies:

  1. f(x) is nonnegative for all x and
  2. The total area under the curve f(x) is one

Dealing with a particular value of the random variable:

Examples of Discrete and Continuous Probability Distributions

Please copmplete your reading of Chapter 3 for class on Wednesday.