The table lists the number of wireless devices per household in a...

5. Binomial Distribution & Discrete Random Variables

Discrete Random Variables

Statistics

5. Binomial Distribution & Discrete Random Variables

Discrete Random Variables

2:19 minutes

Problem 4.Q.2a

Textbook Question

The table lists the number of wireless devices per household in a small town in the United States.

a. Construct a probability distribution.

Verified step by step guidance

Step 1: Calculate the total number of households by summing all the values in the 'Number of households' row. This will be the denominator for calculating probabilities.

Step 2: For each number of wireless devices (0, 1, 2, 3, 4, 5), divide the corresponding number of households by the total number of households to calculate the probability for each outcome. Use the formula: \( P(X = x) = \frac{\text{Number of households for } x}{\text{Total number of households}} \).

Step 3: Construct the probability distribution table. The table should have two columns: one for the number of wireless devices (0, 1, 2, 3, 4, 5) and another for the corresponding probabilities calculated in Step 2.

Step 4: Verify that the sum of all probabilities equals 1. This is a key property of a probability distribution and ensures correctness.

Step 5: Interpret the probability distribution. For example, identify which number of wireless devices is most likely (highest probability) and which is least likely (lowest probability).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability Distribution

A probability distribution describes how the probabilities are distributed over the values of a random variable. In this context, it represents the likelihood of each household having a specific number of wireless devices. The probabilities are calculated by dividing the number of households for each category by the total number of households.

Relative Frequency

Relative frequency is the ratio of the number of times an event occurs to the total number of trials or observations. In constructing a probability distribution from the table, relative frequency is used to determine the probability of each number of wireless devices by taking the count of households for each device number and dividing it by the total number of households.

Cumulative Frequency

Cumulative frequency is the sum of the frequencies for all categories up to a certain point. While not directly required for constructing a basic probability distribution, understanding cumulative frequency can help in analyzing the data further, such as determining the proportion of households with a certain number of devices or fewer.

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The table lists the number of wireless devices per household in a small town in the United States.a. Construct a probability distribution.