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A random experiment refers to a process or action that results in one of many possible outcomes and where the outcome cannot be predicted with certainty before the experiment occurs. In the context of the given example, the random experiment is the measurement of time until a transaction request is made to a computer. The experiment starts at a specific point and continues until the request is logged. Since each new service transaction request represents a different occurrence, repeating the experiment could lead to varying results each time. This uncertainty in the outcome characterizes the process as a random experiment.

In probability, discrete outcomes are a set of distinct and separate results that arise from a random experiment. For our given problem, we deal with discrete outcomes because the measurement of time is taken to the nearest millisecond. Each millisecond marks a separate possible outcome, and these outcomes do not include any values in between. Discreteness in the context of time measurement means that even though the time could technically be any real number, for practical purposes, we only pay attention to whole milliseconds.

Non-negative integers are whole numbers that start at zero and go upward, including numbers like 0, 1, 2, 3, and so on. In the context of our random experiment involving the measurement of time in milliseconds, the sample space is composed of these non-negative integers. This is because time cannot be negative and each integer denotes the counted milliseconds since the experiment began. As these integers represent possible points when the service transaction request is logged, they form the foundational elements of our sample space.

A discrete distribution is a type of probability distribution where the set of outcomes, or sample space, is countable. In our study of the random experiment focusing on time in milliseconds, we assume a discrete distribution because there is an infinite countable set of non-negative integers. Each integer reflects a possible number of milliseconds after the start of observation when a transaction request might occur. The assumption of a discrete distribution indicates that each separate millisecond outcome can have a distinct probability of occurring, although in our example, specific probabilities aren't detailed. This framework helps in modeling and analyzing the probability of events happening at certain times.