Probability & Statistics 2 — Variant 2

The number of accidents per $3$-month period on a certain road has the distribution $\mathrm{Po}(\lambda)$. In the past the value of $\lambda$ has been $5.7$. Following some changes to the road, the council carries out a hypothesis test to determine whether the value of $\lambda$ has decreased. If there are fewer than $3$ accidents in a randomly chosen $3$-month period, the council will conclude that the value of $\lambda$ has decreased.

Find the probability of a Type I error.

Find the probability of a Type II error if the mean number of accidents per $3$-month period is now actually $0.9$.