Chapter 7 Notes. Random Variables and Probability Distributions

Transcription

1 Chapter 7 Notes Random Variables and Probability Distributions Section 7.1 Random Variables Give an example of a discrete random variable. Give an example of a continuous random variable. Exercises # 1, 5, 7 Section 7.2 Probability Distributions for Discrete Random Variables What form does the probability distribution in Example 7.5 Energy Efficient Refrigerators take? Explain how the probability histogram in Example 7.6 Paint Flaws illustrates the properties of a discrete probability distribution. Does the probability distribution in Example 7.7 ipod Shuffles support or refute that the shuffle I truly random? Justify your answer. Exercises # 9, 11, 12, 15, 17, 19 Section 7.3 Probability Distributions for Continuous Random Variables

2 What is the probability distribution for a continuous random variable called? Why is that an appropriate name for the distribution? Compare and contrast the distributions for discrete and continuous random variables? Inspect the graphs and answer the questions that accompany Figure 7.10 before looking at the solutions. Summarize what you learned about the mean and standard deviation of a random variable. Exercises # 20, 22, 23, 24, 26 Section 7.4 Mean and Standard Deviation of a Random Variable Mean Value of a Discrete Random Variable Give two other names for the mean value of a discrete random variable. Explain in words how the mean in calculated. Standard Deviation of a Discrete Random Variable In your own words, what feature of a probability distribution is measured by calculating the variance?

3 In what way is the calculation of the variance similar to that of the mean? Mean and Standard Deviation When x is Continuous What branch of mathematics is useful for calculating the mean and standard deviation of continuous random variables? Mean and Variance of Linear Functions and Linear Combinations Give an example of a linear function of a random variable. Explain in your own words how to obtain the mean and standard deviation for a linear function of a random variable. What is meant by a linear combination of random variables? Provide an example. One Last Note on Linear Functions and Linear Combinations Summarize the concept from this section in the context of Example 7.17 Baggage Weights. Exercises # 27, 29, 30, 34, 35, 37, 41 Section 7.5 Binomial and Geometric Distribution Binomial Distributions Is a binomial random variable discrete or continuous?

4 What key properties define a binomial experiment? How are the terms success and failure used in this context? Geometric Distributions Is a geometric random variable discrete or continuous? What key properties define a geometric experiment? How are the terms success and failure used in this context? Exercises # 44, 48, 49, 52, 53, 54, 56, 58, 60, 61 Section 7.6 Normal Distribution The Standard Normal Distribution How many possible normal curves exist? How many standard normal curves? What kind of function is a normal distribution? (Hint: What is the area under the curve?) What is the difference between the terms (besides the word standard)?

5 What is the meaning of the term standard in this context? What is being standardized? Identifying Extreme Values What is the significance of the values and 1.96 in Examples 7.25 Identifying Extreme Values and 7.26 More Extremes, respectively? Other Normal Distributions What is the meaning and purpose of standardizing the endpoints in a normal distribution? What value in the standard normal distribution corresponds to the mean of the distribution of Newborn Birth Weights found in Example 7.27? What are the standardized endpoints for the interval that represents the middle 95% of the distribution of IQ scores in Figure 7.34? Describing Extreme Values in a Normal Distribution Explain in your own words the algebraic process for obtaining the solution to Example 7.30 Garbage Truck Processing Times. Exercises # 64, 66, 68, 70, 72, 74, 75, 81, 82 Section 7.7 Checking for Normality and Normalizing Transformations Using the Correlation Coefficient to Check Normality What values are paired to create a normal probability plot? What features of a normal probability plot help determine that a normal distribution is plausible?

6 Transforming Data to Obtain a Distribution That Is Approximately Normal What is the purpose of performing a transformation upon a data set? Selecting a Transformation How do you choose a transformation that makes sense? Exercises # 83, 84, 85, 87, 88, 93 Section 7.8 Using the Normal Distribution to Approximate a Discrete Distribution The Normal Curve and Discrete Variables Describe the method and purpose of a continuity correction. Normal Approximation to a Binomial Distribution Is the normal distribution discrete or continuous? What about the binomial distribution? Under what conditions can a binomial distribution be well-approximated by a normal curve? Exercises # 96, 97, 100, 104, 106, 107, 108, 110, 114, 119, 121, 124