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 ?