Exercise 9: Errors in an experimental transmission channel are found when the transmission is
checked by a certifier that detects missing pulses. The number of errors found in an eight bit byte
is a random variable with the following distribution:
Determine each of the following probabilities:
Solution 9: The sum of the probabilities is 1 and all probabilities are greater than or equal to
zero;
pmf: f(1) = 0.7, f(4) = 0.2, f(7) = 0.1
Exercise 10: The number of pages in a PDF document you create has a discrete uniform
distribution from five to ten pages (including the end points). What are the mean and standard
deviation of the number of pages in the document?
Solution 10:
E(X) = (10 + 5)/2 = 7.5, V(X) = [(10 − 5 + 1)2 − 1]/12 = 2.92, σ = 1.709
Exercise 11: This exercise illustrates that poor quality can affect schedules and costs. A
manufacturing process has 120 customer orders to fill. Each order requires one component part
that is purchased from a supplier. However, typically, 2% of the components are identified as
defective, and the components can be assumed to be independent.
(a) If the manufacturer stocks 120 components, what is the probability that the 120 orders can be
filled without reordering components?
(b) If the manufacturer stocks 125 components, what is the probability that the 120 orders can be
filled without reordering components?
(c) If the manufacturer stocks 130 components, what is the probability that the 120 orders can be
filled without reordering components?
Solution 11:
Let X denote the number of defective components among those stocked.
120 
0
120
a) P( X  0)  
  0.02   0.98  0.0885
 0 
125 
125 
 125 
 125 
0
125
1
124
2
123
3
122
b) P( X  5)  
  0.02   0.98   
  0.02   0.98   
  0.02   0.98  
  0.02   0.98 
 0 
 1 
 2 
 3 
125 
 125 
4
121
5
120

  0.02   0.98   
  0.02   0.98  0.9596
 4 
 5 
c) P( X  10)  0.9998
Exercise 12: For a certain manufacturing process, it is known that, on the average, 1 in every 100
items is defective. What is the probability that the fifth item inspected is the first defective item
found?
Solution 12:
Exercise 13: In a manufacturing process where glass products are made, defects or bubbles
occur, occasionally rendering the piece undesirable for marketing. It is known that, on average, 1
in every 1000 of these items produced has one or more bubbles. What is the probability that a
random sample of 8000 will yield fewer than 7 items possessing bubbles?
Solution 13:
Exercise 14: In an NBA (National Basketball Association) championship series, the team that
wins four games out of seven is the winner. Suppose that teams A and B face each other in the
championship games and that team A has probability 0.55 of winning a game over team B.
(a) What is the probability that team A will win the series in 6 games?
(b) What is the probability that team A will win the series?
(c) If teams A and B were facing each other in a regional playoff series, which is decided by
winning three out of five games, what is the probability that team A would win the series?
Solution 14: