d) 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. Note that a discrete random variable X is said to have a Poisson distribution with parameter 1 > 0 if, for k = 0,1,2, ..., the probability mass function of X is given by P ( X = k ) = k! with E(X) = Var (X) = 1. 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