Chapter 7: Random Variables

Key Vocabulary:

§         random variable

§         discrete random variable

§         probability distribution

§         probability histogram

§         density curve

§         probability density curve

§         continuous random variable

§         uniform distribution

§         normal distribution

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§         expected value

§         Law of Large Numbers

§         variance

§         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

(pp.385-402)

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 ?