The probability density function f(y) = aeby - cy² is discussed, with participants questioning whether it represents a normal distribution. It is noted that completing the square in the exponent could suggest a normal distribution, but the function's support being y ∈ (0, ∞) indicates it may be a truncated normal distribution. The conversation highlights the importance of support in determining the classification of probability density functions. Overall, the function's characteristics lead to the conclusion that it is likely a truncated normal distribution.