The following table shows the distribution of the number of televisions per household for residents of a small town:
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### Distribution of Number of Televisions per Household
The table below shows the distribution of the number of televisions per household for residents of a small town:
| X | P(X) |
|----|------|
| 0 | 0.02 |
| 1 | 0.32 |
| 2 | 0.26 |
| 3 | 0.21 |
| 4 | 0.10 |
| 5 | 0.06 |
| 6 | 0.03 |
Where:
- **X** represents the number of televisions in a household.
- **P(X)** represents the probability of a household having X televisions.
#### Problem:
Calculate the average (expected value) number of televisions per household in this town.
#### Options:
- A) 2.00 TVs
- B) 0.39 TVs
- C) None of these are correct
- D) 1.00 TVs
- E) 2.35 TVs
To find the expected value (E[X]) of the number of televisions per household, use the formula:
\[ E[X] = \sum (X \times P(X)) \]
Applying the values from the table:
\[ E[X] = (0 \times 0.02) + (1 \times 0.32) + (2 \times 0.26) + (3 \times 0.21) + (4 \times 0.10) + (5 \times 0.06) + (6 \times 0.03) \]
Calculate each term:
\[ E[X] = 0 + 0.32 + 0.52 + 0.63 + 0.40 + 0.30 + 0.18 \]
Sum the terms:
\[ E[X] = 2.35 \]
Thus, the answer is:
- E) 2.35 TVs](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F133ed738-f4d6-4cad-a3cd-0ebb1624c577%2F50470c45-2046-42ba-90c2-cdf18ba53dd4%2Fdpn3jjl_reoriented.jpeg&w=3840&q=75)
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