In one of the archaeological excavation sites the artifact d

In one of the archaeological excavation sites, the artifact density (# of artifacts per 10 liters of sediment) was 1.5. Suppose you are going to dig up and examine 40 liters of sediment at this site. Let r = 0, 1, 2, 3... be a radom variable that represents the number of prehistoric artifacts found in your 40 liters of sediment. Identify lambda. Round your answer to the nearest tenth.

Solution

here r be a random variable that represents the number of prehistoric artifacts found in 40 liters of sediment.

so r follows a poisson distribution with parameter lambda

now it is known that in 10 liters of sediment the number of artifacts was 1.5

hence in 40 liters of sediment the average number of artifacts is 4*1.5=6

again lambda represents the mean value of r.

hence lambda would be 6 [answer]