9/25/2009

Discussion of Quiz 1 (see p:\data\math\stats\quiz1fall2009-BH.mtw)

Advanced NFL statistics

Questions related to Exam 1

• You may use one 8.5" x 11" formula sheet during the exam.
• You will also have access to our course web page and Minitab during the exam.

Applied Probability Problems (see handout)

Random Variables

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

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

• 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

Our first exam will be next Friday, so there is no weekly homework assignment this week. However, it would be extremely beneficial for you to work on some chapter review exercises.