Error in Anomaly Quiz: question 5

Course Q&A Machine Learning Specialization Unsupervised Learning, Recommenders, Reinforcement
1

Hi,

The question 5 asks “What is the probability of an engine having these two measurements? ( temperature of 17.5 and a vibration of 48)”.
The probability of such a measurement is in fact zero, because the question is asking about a point measurement. The area below a point size data is zero.
The area below the whole bell curve adds up to 1 (the integral is 1). To find a probability of a measurement you have to give a range, like: What is the probability of the temperature being between 16 and 17 and vibration between 47.5 and 48.5, for example. Then you can integrate the curve inside this range for each feature, multiply them, and get the combined probability.
The confusion arises because the graph y axis is labeled P(x) (probability of x) but it is in fact a probability density of x (P(x) per measurement unit). You have to integrate this curve to get the probability, you can’t just read the y axis value to get the probability.

1 Like
2

I would agree with you if the curves in the question were probability density functions.
But they are not.
They are distributions.

3

If you have to integrate the whole function to get probability 100%, then it is a probability density function, which seems to be the case.
Furthermore, the question makes no sense regardless of the graph. How can you answer the question: What is the probability that the temperature today be exactly 22.04328912 degrees? You have to give a range for that kind of question (or assume one implicitly).