2.3 Solve the below problem:

A certain type of tree has seedlings randomly dispersed in a large area, with the mean density of seedlings being approximately three per square yard. If the seedlings are randomly dispersed, 2

the number of seedlings per region, can be modelled as a Poisson random variable. If a forester randomly locates ten 1-square-yard sampling regions in the area, find the probability that none of the regions will contain seedlings and state the moment generating function of the random variable .

3.2 Solve the below problem:

When commercial aircrafts are inspected, wing cracks are reported as non-existent, detectable, or critical. The history of a particular fleet indicates that

=60% of the planes inspected have no wing cracks,

= 30% have detectable wing cracks, and

=10% have critical wing cracks.

Three planes are randomly selected. Find the probability that one has a critical crack, one have detectable cracks, and one have no cracks.