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

        

        

         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 ?