In modeling, it is helpful to frame a variable as either fixed or random. A fixed variable is something like the dosage of a drug in an experiment designed to test how effective that dosage is; it is fixed because data is collected on all possible levels of the dosage, and there is no measurement error. A random variable is something like the level of abstractness of a painting, in which 1 is low, 2 is medium, and 3 is high. It is random because one would want to extrapolate the variable "abstractness" to other values of just 1, 2, and 3 for all pieces of art, and so the values 1, 2, and 3 represent a random sample of all possible other values that the variable abstractness can take on.

Question: Consider a study that administers either 1 mg, 1.5 mg, or 2 mg of a drug to the experimental group and measures some medical output. Under what further circumstances would a fixed effect model be appropriate? Under what further circumstances would a random effects model be appropriate?

Can you please explain why for the example, it is appropriate to use the Probability Distribution of Discrete Random Variable?