Tropical depressions have maximum sustained winds of less than 63 km/hr - Tropical storms have maximum sustained

Fantastic news! We've Found the answer you've been seeking!

Question:

Tropical depressions have maximum sustained winds of less than 63 km/hr - Tropical storms have maximum sustained winds of 63-119 km/hr

- Hurricanes have maximum sustained winds of 119 km/hr or more. Let X be a random variable representing the maximum sustained winds of Atlantic tropical cyclones, that follows the Gamma distribution with the mean of 124 km/hr and the standard deviation of 53 km/hr. Assume that the maximum sustained wind speeds of tropical cyclones are independent of each other.

Use Python to perform all calculations. Provide Python statements and their output.

(d) [7.5 marks] Suppose a particular tropical season has 16 tropical cyclones. Let H be the number of hurricanes in the tropical season. What is the distribution of H? Justify your answer.

(e) [5 marks] Find the probability that at least half of the tropical cyclones are classified as hurricanes.

(f) [10 marks] Simulate a tropical season with 16 tropical cyclones 1 000 000 times by sampling the maximum sustained wind speeds. Determine an empirical estimate of the probability that at least half of the tropical cyclones are classified as hurricanes. How does your empirical estimate compare to the theoretical probability calculated above?

(g) [7.5 marks] Suppose a particular tropical season has 7 hurricanes. Let A be the number of tropical cyclones required in the tropical season to observe 7 hurricanes. What is the distribution of A? Justify your answer.

(h) [5 marks] Find the probability that at least 17 tropical cyclones form for 7 hurricanes to be observed.