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

Question

Question

The daily rainfall in Japan (measured in millimeters) is modelled using a gamma distribution with parameters α = 0.8 and β = 0.4.

Consider the overall rainfall in 365 days, and use mgfs and their properties to prove that this is Ga (292, 0.4).
Use the central limit theorem to approximate the probability that the annual rainfall exceeds 800mm (write down the analytical formula and the R code used to calculate the cdf value).

Answer 1

Answer #1

Answer 2

Similar Homework Help Questions

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

The daily rainfall in Dublin (measured in millimeters) is modelled using a gamma distribution with parameters α = 0.8 and β = 0.4. (a) Write down the distribution (pdf) of the daily rainfall in Dublin. (b) 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 its true counterpart. (c) Consider the overall rainfall in 365 days, and use mgfs and their properties to...
The daily rainfall in Dublin (measured in millimeters) is modelled using a gamma distribution with parameters...

The daily rainfall in Dublin (measured in millimeters) is modelled using a gamma distribution with parameters α = 0.8 and β = 0.4 (d) 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).
1. The daily rainfall in Dublin (measured in millimeters) is modelled using a gamma distribution with...

1. The daily rainfall in Dublin (measured in millimeters) is modelled using a gamma distribution with parameters α = 0.8 and β = 0.4. . (c) Consider the overall rainfall in 365 days, and use mgfs and their properties to prove that this is Ga (292, 0.4). .