Question

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).

Answer 1

If is the random variable representing the daily rainfall, then the random variable representing the annual rainfall is

. Here . Also

According to Central Limit Theorem (CLT), approximately, the distribution of is

The approximate probability that the annual rainfall exceeds 800 mm is

The R commands for the above probability is

> 1-pnorm(800,mean=730,sd=sqrt(1825))
[1] 0.05065079
> 1-pnorm(1.6385761 )
[1] 0.05065079