Reading and Comprehension Questions for Chapter 3
1. Discrete random variables take on values across a continuum.
True
False
False – see Section 3-1.
2. The probability distribution of a discrete random variable is a description of the
probabilities associated with each possible value of the random variable.
True
False
True – see Section 3-2.
3. The sum of all of the probabilities in a probability mass function equals unity.
True
False
True – see Section 3-2.
4. The cumulative distribution function of a discrete random variable is the sum of all of
the probabilities that are less than or equal to x, where x is a specific value of the discrete
random variable X.
True
False
True – see Section 3-3.
5. A cumulative distribution function can be used to find the probability mass function of
a discrete random variable.
True
False
True – see Section 3-3.
6. The mean of a discrete random variable is its expected value.
True
False
True – see Section 3-4.
7. The variance of a discrete random variable is its expected value
True
False
False – see Section 3-4.
8. The standard deviation of a discrete random variable is the square of its variance.
True
False
False – see Section 3-4.
9. A discrete uniform random variable has equal probability assigned to each of its
possible values.
True
False
True – see Section 3-5.
10. If X is a discrete uniform random variable defined on the consecutive integers 10, 11,
…, 20, the mean of X is:
a. 30
b. 15
c. 12
d. None of the above
Answer is b – see Equations 3.6.
11. A Bernoulli trial is a random experiment with only two outcomes, success and failure.
True
False
True – see Section 3-6.
12. The binomial distribution arises from a series of Bernoulli trials.
True
False
True – see Section 3-6.
13. If X is a binomial random variable with n = 20 and p = 0.25, the mean of X is:
a. 10
b. 5
c. 4
d. None of the above
Answer is b – see Equations 3.8
14. The variance of a binomial random variable with parameters n and p is p(1 – p).
True
False
False – see Equations 3.8
15. If X is the number of independent Bernoulli trials until the first success, the
distribution of X is geometric.
True
False
True – see Section 3-7.1.
17. The distribution of the number of Bernoulli trials until the rth success is the negative
binomial distribution.
True
False
False – see Section 3-7.2.
18. The negative binomial distribution has a lack-of memory property.
True
False
False – the lack of memory property is associated with the geometric distribution; see
Section 3-7.1.
19. The hypergeometric distribution is associated with sampling without replacement
from a finite population of N objects.
True
False
True – see Section 3-8.
20. If X is a hypergeometric random variable with parameters n, K, and N, and p = K/N,
the mean and variance of X are:
a. np and np(1 – p)
b. p and np(1 – p)
c. np and p(1 – p)
d. np and np(1 – p)[(N – n)/(N – 1)]
Answer is d; see Equations 3-14.
21. When the sample size n is large relative to the population size N, the binomial
distribution can adequately approximate the hypergeometric distribution.
True
False
False – the binomial distribution can adequately approximate the hypergeeometric
distribution when n is small relative to N.
22. The Poison distribution is a limiting form of the binomial distribution.
True
False
True - see Section 3-9.
23. The Poisson distribution is widely used as a model of the number of events in an
interval.
True
False
True - see Section 3-9.
24. The mean and variance of the Poisson distribution are both equal to the parameter of
the distribution, λ.
True
False
True - see Section 3.9.