Consider the hospital data in Example 2-8 . Suppose a...

Consider the hospital data in Example $2-8 .$ Suppose a patient is selected randomly from the collection in the table. Let $X$ denote the hospital number of the selected patient (either $1,2,3,$ or 4). Does $X$ have a discrete uniform distribution? Why or why not?

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Key Concepts

Discrete Random Variable

A discrete random variable is one that can take on a finite or countable number of distinct outcomes. Here, the hospital number is a discrete random variable because it only assumes specific values corresponding to the hospitals, such as 1, 2, 3, or 4.

Discrete Uniform Distribution

A discrete uniform distribution is a probability distribution where all outcomes have the same likelihood of occurring. For a variable to have a discrete uniform distribution, every possible outcome must have an equal probability.

Weighted Sampling

Weighted sampling occurs when the probability of selecting an outcome is influenced by specific weights, such as the number of patients in a hospital. In the context of the problem, although the outcome is the hospital number, the actual selection probability depends on the number of patients in each hospital, making the distribution non-uniform.

Probability Distribution

A probability distribution describes how probabilities are assigned to the different outcomes of a random variable. In this scenario, understanding the underlying distribution helps determine whether the hospital number follows a uniform pattern or if some hospitals are more frequently represented due to their patient counts.

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