Question

A gardener has a rare orchid plant which flowers only once a year. The flowers produced by the plant could be of any shade of pink but red flowers are considered bad outcomes by the gardener. The number of red flowers the orchid produces follows a Poisson distribution with a mean and variance of 8.

i) Determine the Value at Risk for the number of red flowers produced over the flowering year with a 90% confidence level.

ii) Determine the gardener’s expected shortfall over the flowering year with a 90% confidence level.

Can I get the solutions for this question please?

Answer 1

i)For the value at risk, we need that number of flowers below which the probabillity is equal to 10%

Lets calculate the pmf and cmf upto x=6

P(x<a)=0.1

Hence Value at risk=a-1=4

b)For the exected shortfall, we need to take the weighted average of all the number of flowers less than or equal to 4