This week we continue our study of probability distributions for various discrete and continuous random variables.
If your grade on Test #1 was less than 90%, write out test corrections for any problem for which your score is less than 9 points. Write out the full correct solution on a separate sheet of paper, and turn this in with your original test paper. Do not try to squeeze your corrections into the margins of your original test paper. I will review your corrections, and return these to you. These will be very helpful for you when you study for the Final Exam.
If you did not pass the benchmark test you have an opportunity to re-take it next week (March 10 - 14). If you did pass it, but did not get 100%, you may use this as an opportunity to improve your score on the benchmark. Sign up with me for a time to do this.
The discrete uniform distribution was introduced in Section 5.2. The formula for the discrete uniform probability distribution is on page 190. Review this formula, and check that for any positive integer n the probabilities, f(x), for each possible value of x do meet the criteria for a discrete uniform probability distribution stated on page 189. Notice that the height of the function gives the measure of probability.
The continuous uniform distribution is introduced in Section 6.1. Compare the formula for the uniform probability density function for a continuous variable (given on page 225), with the formula for a discrete variable (page 190). One important distinction between the discrete and continuous random variables is that area (not height) gives a measure of probability. For a continuous random variable, x, we can talk about the probability that x takes on a value over a given interval -- but not about the probability that x takes on a particular discrete value.
Review the calculation of z-scores (page 102), and the empirical rule (page 103). Notice that when we are talking about calculating the mean and standard deviation for a particular sample (as we did in Chapter 3), we use "x-bar" (x with a line over it) and s. However, when we are talking about the theoretical mean and standard deviation for the distribution of a population, we use the Greek letters "mu" and "sigma."
As you read Section 6.2, pay attention to the distinction between the normal distribution and the standard normal distribution.
As you read this section, pay attention to the way that you can use a tree diagram to represent a binomial experiment. Statisticians tend to use the words "success" and "failure" as specialized terms (a kind of statistical jargon). Be sure you understand how these words are being used in this section.
The idea of a binomial experiment will probably seem easier to understand than the formula. It might be simpler to think of this as a two-step process: