The correct answer is option 'D': The sampling distribution is the probability distribution of a statistic. Let's understand this answer in detail.

The concept of sampling distribution is crucial in statistics. It helps us understand the behavior and properties of different statistics that we use to estimate population parameters.

Definition of Sampling Distribution:
- The sampling distribution is a theoretical distribution that represents the possible values of a statistic when repeated random samples are drawn from a population.
- It provides information about the variability of the statistic and allows us to make inferences about the population based on the sample data.

Key Points:
1. Distribution of Sample Observations (Option A):
- The distribution of sample observations refers to the distribution of individual data points within a sample.
- It does not provide information about the behavior of a statistic or its probability distribution.

2. Distribution of Random Samples (Option B):
- The distribution of random samples refers to the collection of all possible samples that can be drawn from a population.
- It helps us understand the variability of sample statistics.
- However, it is not the same as the sampling distribution, which specifically refers to the probability distribution of a statistic.

3. Distribution of a Parameter (Option C):
- A parameter is a numerical value that describes a population.
- The distribution of a parameter is not the same as the sampling distribution.
- The sampling distribution provides information about the behavior of a statistic, which is an estimate of the parameter.

4. Probability Distribution of a Statistic (Option D):
- The probability distribution of a statistic refers to the distribution of all possible values of a statistic that can be calculated from different samples.
- It gives us information about the likelihood of obtaining different values of the statistic.
- The sampling distribution is essential in hypothesis testing, confidence intervals, and estimation of population parameters.

Conclusion:
In summary, the correct answer is option 'D': The sampling distribution is the probability distribution of a statistic. It helps us understand the behavior and variability of statistics that are used to estimate population parameters. Remember that the sampling distribution is different from the distribution of sample observations, distribution of random samples, and distribution of a parameter.