Chapter 7: Random Variables
§ random variable
§ discrete random variable
§ probability distribution
§ probability histogram
§ density curve
§ probability density curve
§ continuous random variable
§ uniform distribution
§ normal distribution
§ expected value
§ Law of Large Numbers
§ standard deviation
7.1 Discrete and Continuous Random Variables (pp.367-379)
1. What is a discrete random variable?
2. If X is a discrete random variable, what information does the probability distribution of X give?
3. In a probability histogram what does the height of each bar represent?
4. In a probability histogram what is the sum of the height of each bar?
5. What is a continuous random variable?
6. If X is a discrete random variable, how is the probability distribution of X described?
7. What is the area under a probability density curve equal to?
8. What is the difference between a discrete random variable and a continuous random variable?
9. If X is a discrete random variable, do and have the same value? Explain.
10. If X is a continuous random variable, do and have the same value? Explain.
11. How is a normal distribution related to probability distribution?
12. If a normal distribution is always a probability distribution, is a probability distribution always a normal distribution?
7.2 Means and Variances of Random Variables
1. Explain the difference between the notations and .
2. What is meant by the expected value of X ?
3. How do you calculate the mean of a discrete random variable X ?
4. Explain the Law of Large Numbers.
5. Suppose = 5 and = 10. According to the rules for means, what is ?
6. Suppose = 2. According to the rules for means, what is ?
7. Explain how to calculate the variance of a discrete random variable X using the formula .
8. Given the variance of a random variable, explain how to calculate the standard deviation.
9. Suppose = 2 and = 3 and X and Y are independent random variables. According to the rules for variances, what is ? What is ?
10. Suppose = 4. According to the rules for variances, what is ? What is ?