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The daily rainfall in Cork (measured in millimeters) is modelled using a gamma distribution with parameters...

The daily rainfall in Cork (measured in millimeters) is modelled using a gamma distribution with parameters α = 0.8 and β = 0.3.

1) Use Markov’s inequality to upper bound the probability that the observed rainfall in a given day is larger than 3 mm, and compare the value to the result of cdf calculation.

2) Consider the overall rainfall in 365 days, and use moment generating functions and their properties to prove that this is Ga (292, 0.3).

3) Use the central limit theorem to approximate the probability that the annual rainfall exceeds 800mm (write down the analytical formula and the code used to calculate the cdf value).

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orchestra answered 1 year ago
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