The Flaw of Averages suggests that using the average (expected values) of distributions of uncertain variables to determine some complex outcome can be deceiving and incorrect. Consider a simple model where the variable of interest is Revenue (R). It is calculated by multiplying the randomly determined input, demand (D) in units, by the randomly determined input unit price (P), or R = D X P. This logic makes sense. Assume that both input variables are normally distributed and that the random occurrence of negative values for D and P from the normal distributions, though possible, make no sense. Thus, they are replaced by "0" values.
Categorize the following statements as true or false:
a) Regardless of the mean and standard deviation of the normally distributed inputs in our problem above, it is correct to assume that the average of µR is equal to the average of µDX µP. [ Select ] ["True", "False"]
b) If the standard deviations of the normally distributed inputs are large relative to their means (µ = σ), then the µR will be lower than µD X µP. [ Select ] ["True", "False"]