Discussion of Applied Probability Problems from handout
What's the difference between events that are independent and disjoint (mutually exclusive)?
- Independent events can both happen, both not happen, or happen separately.
- Disjoint events can only happen separately.
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:
- pi is in the interval [0, 1] for each i and
- 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:
- f(x) is nonnegative for all x and
- The total area under the curve f(x) is one
Dealing with a particular value of the random variable:
- For discrete random variables, the equality sign is very important. In general, the probability that X is at most c is not equal to the probability that X is less than c.
- The probability model for continuous random variables assigns probabilities to intervals of outcomes, not to individual outcomes. Thus, the probability that X is at most c is equal to the probability that X is less than c.
Examples of Discrete and Continuous Probability Distributions
- Class Exercises - see handout
Please copmplete your reading of Chapter 3 for class on Wednesday.