1. Unit 4 Review

2. Starter Write the characteristics of the binomial setting. What is the difference between the binomial setting and the geometric setting?

3. Answer The binomial setting has 4 characteristics: –There are only two possible outcomes –Each trial has fixed probability of success –Each trial is independent of all other trials –There are a fixed number of trials; the variable of interest is the number of successes The geometric setting has the same first three characteristics. The difference is in the fourth: there are an unknown number of trials; trials stop after the first success; the variable of interest is the number of trials until the first success

4. Discrete and Continuous Random Variables Section 7.1 Given the definition of a discrete Random Variable, write a Probability Distribution Function (PDF) or Cumulative Distribution Function (CDF) as either a table or a histogram. Display the PDF of a continuous random variable as a density curve. Find the probability that a given continuous random variable is within a specified interval by finding the area under a density curve. –For geometrically defined curves, use formulas –For normal distribution curves, use normalcdf function or z-score and Table A

5. Means and Variances of Random Variables Section 7.2 Find the mean of a discrete random variable from formula and on calculator Calculate the variance and standard deviation of a discrete random variable from formula and calculator Find the mean and variance of a random variable formed from a linear transformation of a given random variable with known mean and variance. Find the mean and variance of a random variable formed from a linear combination of two given random variables with known mean and variance.

6. The Binomial Distribution Section 8.1 Identify whether a random variable is in a binomial setting. Use TI-83 or the binomial probability formula to find binomial probabilities and construct probability distribution tables and histograms. Calculate cumulative distribution functions for binomial random variables and construct cumulative distribution tables and histograms. Calculate the mean (expected value) and standard deviation (and variance) of a given binomial random variable from formulas and on calculator.

7. The Geometric Distribution Section 8.2 Identify whether a random variable is in a geometric setting. Use formulas or a TI-83 to determine geometric probabilities and construct probability distribution tables and histograms. Calculate cumulative distribution functions for geometric random variables and construct cumulative distribution tables and histograms. Calculate the mean (expected value) of a given geometric random variable.