Reading and Comprehension Questions for Chapter 4
1. Continuous random variables take on discrete values.
True
False
False – see Section 4-1.
2. The probability density function of a continuous random variable is a simple
description of the probabilities associated with the random variable.
True
False
True – see Section 4-2.
3. The sum of all of the probabilities associated with each specific value of a continuous
random variable equals unity.
True
False
False – see Section 4-2.
4. The cumulative distribution function of a continuous random variable is the probability
that the random variable X is greater than or equal to x, where x is a specific value of the
continuous random variable X.
True
False
False – see Section 4-3.
5. A cumulative distribution function can be used to find the probability density function
of a discrete random variable.
True
False
True – see Section 4-3.
6. The mean of a continuous random variable is its expected value.
True
False
True – see Section 4-4.
7. The standard deviation of a continuous random variable is its expected value.
True
False
False – see Section 4-4.
8. The variance of a discrete random variable is defined as  
2

 (x  )
2
f ( x)dx .

True
False
True – see Section 4-4.
9. The variance of a continuous random variable can be written as either
 
2

 (x  )
2
f ( x)dx or  
2

True

x
2
f ( x)dx   2 .

False
True – see Section 4-4.
10. If X is a continuous uniform random variable defined over the range 10 to 20, the
mean of X is:
a. 12
b. 15
c. 16
d. None of the above
Answer is b; see Equations 4-7.
11. The normal distribution has two parameters; the mean μ, and the variance σ2.
True
False
True – see Section 4-6.
12. The standard normal distribution has both mean and variance equal to unity.
True
False
False – see Section 4-6.
13. If X is a normal random variable that has mean μ = 20 and standard deviation σ = 2,
the standardized value of X = 16 is
a. 4
b. -2
c. 2
d. -4
e. None of the above
Answer is b; see Equation 4-10
14. To standardize a normal random variable that has mean μ and variance σ2 we used the
X 
formula Z 
.
2
True
False
False – see Equation 4-10.
15. The normal distribution can be used to approximate the binomial distribution if np
and n(1-p) are greater than five.
True
False
True – see Section 4-7.
17. The exponential random variable models the distance between successive events in a
Poisson process.
True
False
True – see Section 4-8.
18. In the exponential distribution with parameter λ, the mean and variance are both equal
to λ.
True
False
False – see Equation 4-15.
19. The exponential distribution has a lack of memory property.
True
False
True – see Section 4-8.
20. The Erlang and exponential distributions are special cases of the gamma distribution.
True False
True – see section 4-9.
21. The Weibull distribution is often used to model the time to failure in reliability
engineering work.
True
False
True – see Section 4-10.
22. A random variable that is the natural logarithm of a normal random variable is called
a lognormal random variable.
True
False
True - see Section 4-11.