Questions

1. The probability that a person is 1.70 m tall is p(Tall) = 0.75, while the probability that tomorrow it's going to rain is P(Rain) = 0.2. What is the probability P(Tall, Rain)? (that is, the probability that a person is 1.70 m tall and tomorrow it's going to rain).
2. Given a dataset X, we build an histogram with 1,000 bins and we find that many of them are empty. Why does this happen?
3. A histogram contains three bins with, respectively 20, 30, and 25 samples. The first bin has a range 0 < x < 2, the second 2 < x < 4, and the third 4 < x < 6. What is the approximate probability that P(x) > 2?
4. Given a normal distribution N(0, 1), can a sample x with p(x) = 0.35 be considered as an anomaly?
5. A dataset X with 500 samples has std(X) = 2.5 and IQR(X) = 3.0. What is the optimal bandwidth?
6. An expert told us that a distribution is extremely peaked around...