Homework Help is Here – Start Your Trial Now!
Math
Probability
Watershed is a media services company that provides online streaming movie and television content. As a result of the competitive market of streaming service providers, Watershed is interested in proactively identifying will unsubscribe in the next three months based on the customer's characteristics. For a test set of customers, the file Watershed contains an indication of whether a customer unsubscribed in the past three months and the classification model's estimated unsubscribe probability for the customer. In an effort to prevent customer churn, Watershed wishes to offer promotions to customers who may unsubscribe. It costs Watershed $15 to offer a promotion to a customer. If offered a promotion, it successfully persuades a customer to remain a Watershed customer with probability 0.8, and the retaining the customer is worth $55 to Watershed. Assuming customers will be offered the promotion in order of decreasing estimated unsubscribe probability; determine how many customers Watershed should offer the promotion to maximize the profit of the intervention campaign. Compute the average profit from offering the top n customers a promotion as:   Profit = Number of unsubscribing customers in top n       × (P(unsubscribing customer persuaded to remain) × (55 - 15)       + P(unsubscribing customer is not persuaded) × (0 - 15))       + Number of customers who don't intend to unsubscribe × (0 - 15)   Customer Unsubscribe? Probability of Unsubscribe 57 0 0.99 111 0 0.99 141 1 0.99 158 0 0.99 180 1 0.99 119 1 0.98 140 1 0.98 191 1 0.98 31 0 0.97 33 0 0.97 58 0 0.97 71 1 0.97 121 1 0.97 96 1 0.95 131 0 0.95 197 0 0.95 7 0 0.93 26 1 0.93 116 1 0.93 15 0 0.92 56 1 0.92 130 0 0.92 149 0 0.92 178 0 0.92 44 0 0.91 66 1 0.91 9 0 0.90 76 0 0.89 148 0 0.89 172 0 0.89 5 0 0.88 11 1 0.88 91 0 0.88 133 0 0.88 147 0 0.88 54 1 0.87 194 0 0.87 18 0 0.86 120 1 0.85 150 0 0.85 64 1 0.84 69 0 0.84 139 1 0.84 1 0 0.83 127 1 0.83 157 0 0.83 177 0 0.83 145 0 0.82 94 1 0.81 87 1 0.80 124 1 0.80 100 0 0.79 104 0 0.79 129 0 0.79 152 1 0.79 184 0 0.79 78 0 0.78 199 1 0.78 105 0 0.77 108 0 0.76 93 0 0.74 161 1 0.74 144 0 0.73 75 0 0.71 84 0 0.71 19 1 0.70 135 1 0.70 200 0 0.70 14 0 0.69 167 0 0.69 99 0 0.68 151 0 0.68 195 0 0.68 51 0 0.67 67 1 0.67 49 1 0.65 23 0 0.64 61 1 0.63 36 0 0.62 183 1 0.62 160 1 0.61 110 0 0.60 159 0 0.60 198 0 0.60 102 1 0.58 25 0 0.57 55 0 0.57 70 0 0.57 163 0 0.57 12 0 0.56 176 0 0.56 187 0 0.56 28 0 0.54 34 0 0.54 98 0 0.54 138 0 0.54 27 0 0.52 3 0 0.51 85 0 0.51 128 0 0.51 103 0 0.50 63 0 0.49 68 0 0.49 115 0 0.49 155 0 0.48 113 0 0.47 60 0 0.46 171 0 0.46 37 1 0.45 17 0 0.44 101 0 0.44 80 0 0.43 132 0 0.43 134 0 0.43 142 0 0.43 29 1 0.42 107 1 0.42 8 0 0.41 189 0 0.40 32 0 0.39 73 0 0.39 35 1 0.38 52 0 0.38 114 0 0.38 125 0 0.38 186 0 0.38 6 0 0.37 74 0 0.37 95 0 0.37 185 0 0.37 16 0 0.36 20 0 0.36 136 0 0.36 192 0 0.36 10 0 0.35 143 0 0.33 156 0 0.33 181 0 0.33 45 0 0.29 62 0 0.29 86 0 0.29 170 0 0.29 46 0 0.28 168 0 0.27 196 0 0.27 59 0 0.26 106 0 0.26 179 0 0.26 175 0 0.25 88 0 0.24 47 0 0.23 48 0 0.23 4 0 0.21 50 0 0.21 13 0 0.20 41 0 0.19 79 0 0.17 89 0 0.17 123 0 0.17 162 1 0.17 30 0 0.16 117 0 0.16 24 0 0.15 65 0 0.15 137 0 0.15 173 0 0.15 39 0 0.14 82 0 0.14 165 0 0.14 21 0 0.13 90 0 0.13 166 0 0.13 118 0 0.12 193 0 0.12 126 0 0.11 154 0 0.11 146 0 0.10 190 0 0.10 2 1 0.09 53 0 0.08 81 0 0.08 22 0 0.07 109 0 0.07 153 0 0.07 182 0 0.07 40 0 0.06 42 0 0.06 43 0 0.06 164 0 0.06 77 0 0.05 174 0 0.05 38 0 0.04 92 0 0.04 188 0 0.04 97 0 0.03 122 0 0.03 72 0 0.02 83 0 0.02 112 0 0.01 169 0 0.01

Watershed is a media services company that provides online streaming movie and television content. As a result of the competitive market of streaming service providers, Watershed is interested in proactively identifying will unsubscribe in the next three months based on the customer's characteristics. For a test set of customers, the file Watershed contains an indication of whether a customer unsubscribed in the past three months and the classification model's estimated unsubscribe probability for the customer. In an effort to prevent customer churn, Watershed wishes to offer promotions to customers who may unsubscribe. It costs Watershed $15 to offer a promotion to a customer. If offered a promotion, it successfully persuades a customer to remain a Watershed customer with probability 0.8, and the retaining the customer is worth $55 to Watershed. Assuming customers will be offered the promotion in order of decreasing estimated unsubscribe probability; determine how many customers Watershed should offer the promotion to maximize the profit of the intervention campaign. Compute the average profit from offering the top n customers a promotion as:   Profit = Number of unsubscribing customers in top n       × (P(unsubscribing customer persuaded to remain) × (55 - 15)       + P(unsubscribing customer is not persuaded) × (0 - 15))       + Number of customers who don't intend to unsubscribe × (0 - 15)   Customer Unsubscribe? Probability of Unsubscribe 57 0 0.99 111 0 0.99 141 1 0.99 158 0 0.99 180 1 0.99 119 1 0.98 140 1 0.98 191 1 0.98 31 0 0.97 33 0 0.97 58 0 0.97 71 1 0.97 121 1 0.97 96 1 0.95 131 0 0.95 197 0 0.95 7 0 0.93 26 1 0.93 116 1 0.93 15 0 0.92 56 1 0.92 130 0 0.92 149 0 0.92 178 0 0.92 44 0 0.91 66 1 0.91 9 0 0.90 76 0 0.89 148 0 0.89 172 0 0.89 5 0 0.88 11 1 0.88 91 0 0.88 133 0 0.88 147 0 0.88 54 1 0.87 194 0 0.87 18 0 0.86 120 1 0.85 150 0 0.85 64 1 0.84 69 0 0.84 139 1 0.84 1 0 0.83 127 1 0.83 157 0 0.83 177 0 0.83 145 0 0.82 94 1 0.81 87 1 0.80 124 1 0.80 100 0 0.79 104 0 0.79 129 0 0.79 152 1 0.79 184 0 0.79 78 0 0.78 199 1 0.78 105 0 0.77 108 0 0.76 93 0 0.74 161 1 0.74 144 0 0.73 75 0 0.71 84 0 0.71 19 1 0.70 135 1 0.70 200 0 0.70 14 0 0.69 167 0 0.69 99 0 0.68 151 0 0.68 195 0 0.68 51 0 0.67 67 1 0.67 49 1 0.65 23 0 0.64 61 1 0.63 36 0 0.62 183 1 0.62 160 1 0.61 110 0 0.60 159 0 0.60 198 0 0.60 102 1 0.58 25 0 0.57 55 0 0.57 70 0 0.57 163 0 0.57 12 0 0.56 176 0 0.56 187 0 0.56 28 0 0.54 34 0 0.54 98 0 0.54 138 0 0.54 27 0 0.52 3 0 0.51 85 0 0.51 128 0 0.51 103 0 0.50 63 0 0.49 68 0 0.49 115 0 0.49 155 0 0.48 113 0 0.47 60 0 0.46 171 0 0.46 37 1 0.45 17 0 0.44 101 0 0.44 80 0 0.43 132 0 0.43 134 0 0.43 142 0 0.43 29 1 0.42 107 1 0.42 8 0 0.41 189 0 0.40 32 0 0.39 73 0 0.39 35 1 0.38 52 0 0.38 114 0 0.38 125 0 0.38 186 0 0.38 6 0 0.37 74 0 0.37 95 0 0.37 185 0 0.37 16 0 0.36 20 0 0.36 136 0 0.36 192 0 0.36 10 0 0.35 143 0 0.33 156 0 0.33 181 0 0.33 45 0 0.29 62 0 0.29 86 0 0.29 170 0 0.29 46 0 0.28 168 0 0.27 196 0 0.27 59 0 0.26 106 0 0.26 179 0 0.26 175 0 0.25 88 0 0.24 47 0 0.23 48 0 0.23 4 0 0.21 50 0 0.21 13 0 0.20 41 0 0.19 79 0 0.17 89 0 0.17 123 0 0.17 162 1 0.17 30 0 0.16 117 0 0.16 24 0 0.15 65 0 0.15 137 0 0.15 173 0 0.15 39 0 0.14 82 0 0.14 165 0 0.14 21 0 0.13 90 0 0.13 166 0 0.13 118 0 0.12 193 0 0.12 126 0 0.11 154 0 0.11 146 0 0.10 190 0 0.10 2 1 0.09 53 0 0.08 81 0 0.08 22 0 0.07 109 0 0.07 153 0 0.07 182 0 0.07 40 0 0.06 42 0 0.06 43 0 0.06 164 0 0.06 77 0 0.05 174 0 0.05 38 0 0.04 92 0 0.04 188 0 0.04 97 0 0.03 122 0 0.03 72 0 0.02 83 0 0.02 112 0 0.01 169 0 0.01

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
See similar textbooks
icon
Related questions
Question

Watershed is a media services company that provides online streaming movie and television content. As a result of the competitive market of streaming service providers, Watershed is interested in proactively identifying will unsubscribe in the next three months based on the customer's characteristics. For a test set of customers, the file Watershed contains an indication of whether a customer unsubscribed in the past three months and the classification model's estimated unsubscribe probability for the customer. In an effort to prevent customer churn, Watershed wishes to offer promotions to customers who may unsubscribe. It costs Watershed $15 to offer a promotion to a customer. If offered a promotion, it successfully persuades a customer to remain a Watershed customer with probability 0.8, and the retaining the customer is worth $55 to Watershed.

Assuming customers will be offered the promotion in order of decreasing estimated unsubscribe probability; determine how many customers Watershed should offer the promotion to maximize the profit of the intervention campaign. Compute the average profit from offering the top n customers a promotion as:

  Profit = Number of unsubscribing customers in top n
      × (P(unsubscribing customer persuaded to remain) × (55 - 15)
      + P(unsubscribing customer is not persuaded) × (0 - 15))
      + Number of customers who don't intend to unsubscribe × (0 - 15)

 

Customer Unsubscribe? Probability of Unsubscribe
57 0 0.99
111 0 0.99
141 1 0.99
158 0 0.99
180 1 0.99
119 1 0.98
140 1 0.98
191 1 0.98
31 0 0.97
33 0 0.97
58 0 0.97
71 1 0.97
121 1 0.97
96 1 0.95
131 0 0.95
197 0 0.95
7 0 0.93
26 1 0.93
116 1 0.93
15 0 0.92
56 1 0.92
130 0 0.92
149 0 0.92
178 0 0.92
44 0 0.91
66 1 0.91
9 0 0.90
76 0 0.89
148 0 0.89
172 0 0.89
5 0 0.88
11 1 0.88
91 0 0.88
133 0 0.88
147 0 0.88
54 1 0.87
194 0 0.87
18 0 0.86
120 1 0.85
150 0 0.85
64 1 0.84
69 0 0.84
139 1 0.84
1 0 0.83
127 1 0.83
157 0 0.83
177 0 0.83
145 0 0.82
94 1 0.81
87 1 0.80
124 1 0.80
100 0 0.79
104 0 0.79
129 0 0.79
152 1 0.79
184 0 0.79
78 0 0.78
199 1 0.78
105 0 0.77
108 0 0.76
93 0 0.74
161 1 0.74
144 0 0.73
75 0 0.71
84 0 0.71
19 1 0.70
135 1 0.70
200 0 0.70
14 0 0.69
167 0 0.69
99 0 0.68
151 0 0.68
195 0 0.68
51 0 0.67
67 1 0.67
49 1 0.65
23 0 0.64
61 1 0.63
36 0 0.62
183 1 0.62
160 1 0.61
110 0 0.60
159 0 0.60
198 0 0.60
102 1 0.58
25 0 0.57
55 0 0.57
70 0 0.57
163 0 0.57
12 0 0.56
176 0 0.56
187 0 0.56
28 0 0.54
34 0 0.54
98 0 0.54
138 0 0.54
27 0 0.52
3 0 0.51
85 0 0.51
128 0 0.51
103 0 0.50
63 0 0.49
68 0 0.49
115 0 0.49
155 0 0.48
113 0 0.47
60 0 0.46
171 0 0.46
37 1 0.45
17 0 0.44
101 0 0.44
80 0 0.43
132 0 0.43
134 0 0.43
142 0 0.43
29 1 0.42
107 1 0.42
8 0 0.41
189 0 0.40
32 0 0.39
73 0 0.39
35 1 0.38
52 0 0.38
114 0 0.38
125 0 0.38
186 0 0.38
6 0 0.37
74 0 0.37
95 0 0.37
185 0 0.37
16 0 0.36
20 0 0.36
136 0 0.36
192 0 0.36
10 0 0.35
143 0 0.33
156 0 0.33
181 0 0.33
45 0 0.29
62 0 0.29
86 0 0.29
170 0 0.29
46 0 0.28
168 0 0.27
196 0 0.27
59 0 0.26
106 0 0.26
179 0 0.26
175 0 0.25
88 0 0.24
47 0 0.23
48 0 0.23
4 0 0.21
50 0 0.21
13 0 0.20
41 0 0.19
79 0 0.17
89 0 0.17
123 0 0.17
162 1 0.17
30 0 0.16
117 0 0.16
24 0 0.15
65 0 0.15
137 0 0.15
173 0 0.15
39 0 0.14
82 0 0.14
165 0 0.14
21 0 0.13
90 0 0.13
166 0 0.13
118 0 0.12
193 0 0.12
126 0 0.11
154 0 0.11
146 0 0.10
190 0 0.10
2 1 0.09
53 0 0.08
81 0 0.08
22 0 0.07
109 0 0.07
153 0 0.07
182 0 0.07
40 0 0.06
42 0 0.06
43 0 0.06
164 0 0.06
77 0 0.05
174 0 0.05
38 0 0.04
92 0 0.04
188 0 0.04
97 0 0.03
122 0 0.03
72 0 0.02
83 0 0.02
112 0 0.01
169 0 0.01

The maximum profit of $ _____ occurs when _____ customers are offered the promotion.

Watershed is a media services company that provides online streaming movie and television content. As a result of the competitive market of streaming service providers, Watershed is interested in proactively identifying which customers will unsubscribe in the next three months based on the customer's characteristics. For a test set of customers, the file Watershed contains an indication of whether a customer unsubscribed in the past three months and the classification model's estimated unsubscribe probability for the customer. In an effort to prevent customer churn, Watershed wishes to offer promotions to customers who may unsubscribe. It costs Watershed $15 to offer a promotion to a customer. If offered a promotion, it successfully persuades a customer to remain a Watershed customer with probability 0.8, and retaining the customer is worth $55 to Watershed. Click on the datafile logo to reference the data. --- **DATA** Assuming customers will be offered the promotion in order of decreasing estimated unsubscribe probability; determine how many customers Watershed should offer the promotion to maximize the profit of the intervention campaign. Compute the average profit from offering the top \( n \) customers a promotion as: \[ \text{Profit} = \text{Number of unsubscribing customers in top } n \] \[ \times \left( \text{P(unsubscribing customer persuaded to remain)} \times (55 - 15)\right) \] \[ + \left(\text{P(unsubscribing customer is not persuaded)} \times (0 - 15)\right) \] \[ + \text{Number of customers who don’t intend to unsubscribe} \times (0 - 15) \] The maximum profit of \(\$\_\_\_\_\) occurs when \(\_\_\_\_\) customers are offered the promotion.
Transcribed Image Text:Watershed is a media services company that provides online streaming movie and television content. As a result of the competitive market of streaming service providers, Watershed is interested in proactively identifying which customers will unsubscribe in the next three months based on the customer's characteristics. For a test set of customers, the file Watershed contains an indication of whether a customer unsubscribed in the past three months and the classification model's estimated unsubscribe probability for the customer. In an effort to prevent customer churn, Watershed wishes to offer promotions to customers who may unsubscribe. It costs Watershed $15 to offer a promotion to a customer. If offered a promotion, it successfully persuades a customer to remain a Watershed customer with probability 0.8, and retaining the customer is worth $55 to Watershed. Click on the datafile logo to reference the data. --- **DATA** Assuming customers will be offered the promotion in order of decreasing estimated unsubscribe probability; determine how many customers Watershed should offer the promotion to maximize the profit of the intervention campaign. Compute the average profit from offering the top \( n \) customers a promotion as: \[ \text{Profit} = \text{Number of unsubscribing customers in top } n \] \[ \times \left( \text{P(unsubscribing customer persuaded to remain)} \times (55 - 15)\right) \] \[ + \left(\text{P(unsubscribing customer is not persuaded)} \times (0 - 15)\right) \] \[ + \text{Number of customers who don’t intend to unsubscribe} \times (0 - 15) \] The maximum profit of \(\$\_\_\_\_\) occurs when \(\_\_\_\_\) customers are offered the promotion.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

Watershed is a media services company that provides online streaming movie and television content. As a result of the competitive market of streaming service providers, Watershed is interested in proactively identifying will unsubscribe in the next three months based on the customer's characteristics. For a test set of customers, the file Watershed contains an indication of whether a customer unsubscribed in the past three months and the classification model's estimated unsubscribe probability for the customer. In an effort to prevent customer churn, Watershed wishes to offer promotions to customers who may unsubscribe. It costs Watershed $15 to offer a promotion to a customer. If offered a promotion, it successfully persuades a customer to remain a Watershed customer with probability 0.7, and the retaining the customer is worth $60 to Watershed.

Click on the datafile logo to reference the data.

 

Assuming customers will be offered the promotion in order of decreasing estimated unsubscribe probability; determine how many customers Watershed should offer the promotion to maximize the profit of the intervention campaign. Compute the average profit from offering the top n customers a promotion as:

 

  Profit = Number of unsubscribing customers in top n
      × (P(unsubscribing customer persuaded to remain) × (60 - 15)
      + P(unsubscribing customer is not persuaded) × (0 - 15))
      + Number of customers who don't intend to unsubscribe × (0 - 15)

 

The maximum profit of $    occurs when   customers are offered the promotion.

 

Customer Unsubscribe? Probability of Unsubscribe  
57 0 0.99  
111 0 0.99  
141 1 0.99  
158 0 0.99  
180 1 0.99  
119 1 0.98  
140 1 0.98  
191 1 0.98  
31 0 0.97  
33 0 0.97  
58 0 0.97  
71 1 0.97  
121 1 0.97  
96 1 0.95  
131 0 0.95  
197 0 0.95  
7 0 0.93  
26 1 0.93  
116 1 0.93  
15 0 0.92  
56 1 0.92  
130 0 0.92  
149 0 0.92  
178 0 0.92  
44 0 0.91  
66 1 0.91  
9 0 0.90  
76 0 0.89  
148 0 0.89  
172 0 0.89  
5 0 0.88  
11 1 0.88  
91 0 0.88  
133 0 0.88  
147 0 0.88  
54 1 0.87  
194 0 0.87  
18 0 0.86  
120 1 0.85  
150 0 0.85  
64 1 0.84  
69 0 0.84  
139 1 0.84  
1 0 0.83  
127 1 0.83  
157 0 0.83  
177 0 0.83  
145 0 0.82  
94 1 0.81  
87 1 0.80  
124 1 0.80  
100 0 0.79  
104 0 0.79  
129 0 0.79  
152 1 0.79  
184 0 0.79  
78 0 0.78  
199 1 0.78  
105 0 0.77  
108 0 0.76  
93 0 0.74  
161 1 0.74  
144 0 0.73  
75 0 0.71  
84 0 0.71  
19 1 0.70  
135 1 0.70  
200 0 0.70  
14 0 0.69  
167 0 0.69  
99 0 0.68  
151 0 0.68  
195 0 0.68  
51 0 0.67  
67 1 0.67  
49 1 0.65  
23 0 0.64  
61 1 0.63  
36 0 0.62  
183 1 0.62  
160 1 0.61  
110 0 0.60  
159 0 0.60  
198 0 0.60  
102 1 0.58  
25 0 0.57  
55 0 0.57  
70 0 0.57  
163 0 0.57  
12 0 0.56  
176 0 0.56  
187 0 0.56  
28 0 0.54  
34 0 0.54  
98 0 0.54  
138 0 0.54  
27 0 0.52  
3 0 0.51  
85 0 0.51  
128 0 0.51  
103 0 0.50  
63 0 0.49  
68 0 0.49  
115 0 0.49  
155 0 0.48  
113 0 0.47  
60 0 0.46  
171 0 0.46  
37 1 0.45  
17 0 0.44  
101 0 0.44  
80 0 0.43  
132 0 0.43  
134 0 0.43  
142 0 0.43  
29 1 0.42  
107 1 0.42  
8 0 0.41  
189 0 0.40  
32 0 0.39  
73 0 0.39  
35 1 0.38  
52 0 0.38  
114 0 0.38  
125 0 0.38  
186 0 0.38  
6 0 0.37  
74 0 0.37  
95 0 0.37  
185 0 0.37  
16 0 0.36  
20 0 0.36  
136 0 0.36  
192 0 0.36  
10 0 0.35  
143 0 0.33  
156 0 0.33  
181 0 0.33  
45 0 0.29  
62 0 0.29  
86 0 0.29  
170 0 0.29  
46 0 0.28  
168 0 0.27  
196 0 0.27  
59 0 0.26  
106 0 0.26  
179 0 0.26  
175 0 0.25  
88 0 0.24  
47 0 0.23  
48 0 0.23  
4 0 0.21  
50 0 0.21  
13 0 0.20  
41 0 0.19  
79 0 0.17  
89 0 0.17  
123 0 0.17  
162 1 0.17  
30 0 0.16  
117 0 0.16  
24 0 0.15  
65 0 0.15  
137 0 0.15  
173 0 0.15  
39 0 0.14  
82 0 0.14  
165 0 0.14  
21 0 0.13  
90 0 0.13  
166 0 0.13  
118 0 0.12  
193 0 0.12  
126 0 0.11  
154 0 0.11  
146 0 0.10  
190 0 0.10  
2 1 0.09  
53 0 0.08  
81 0 0.08  
22 0 0.07  
109 0 0.07  
153 0 0.07  
182 0 0.07  
40 0 0.06  
42 0 0.06  
43 0 0.06  
164 0 0.06  
77 0 0.05  
174 0 0.05  
38 0 0.04  
92 0 0.04  
188 0 0.04  
97 0 0.03  
122 0 0.03  
72 0 0.02  
83 0 0.02  
112 0 0.01  
169 0 0.01  
       
Solution
Bartleby Expert
SEE SOLUTION
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON
SEE MORE TEXTBOOKS