1) At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was1.1. Suppose you are going to dig up and examine42liters of sediment at this site. Letr= 0, 1, 2, 3, ... be a random variable that represents the number of prehistoric artifacts found in your42liters of sediment.

(a) Explain why the Poisson distribution would be a good choice for the probability distribution ofr.

Finding prehistoric artifacts is a rare occurrence. It is reasonable to assume the events are independent.

Finding prehistoric artifacts is a rare occurrence. It is reasonable to assume the events are dependent.

Finding prehistoric artifacts is a common occurrence. It is reasonable to assume the events are independent.

Finding prehistoric artifacts is a common occurrence. It is reasonable to assume the events are dependent.

What is?

Write out the formula for the probability distribution of the random variabler. (Usee,, andrin your answer.)

P(r) =

(b) Compute the probabilities that in your42liters of sediment you will find two prehistoric artifacts, three prehistoric artifacts, and four prehistoric artifacts.

P(2) =

P(3) =

P(4) =

(c) Find the probability that you will find three or more prehistoric artifacts in the42liters of sediment.

(d) Find the probability that you will find fewer than three prehistoric artifacts in the42liters of sediment.

2)In his doctoral thesis, L. A. Beckel (University of Minnesota, 1982) studied the social behavior of river otters during the mating season. An important role in the bonding process of river otters is very short periods of social grooming. After extensive observations, Dr. Beckel found that one group of river otters under study had a frequency of initiating grooming of approximately 1.7 for each 10 minutes. Suppose that you are observing river otters for30minutes. Letr= 0, 1, 2, ... be a random variable that represents the number of times (in a30-minute interval) one otter initiates social grooming of another.

(a) Explain why the Poisson distribution would be a good choice for the probability distribution ofr.

Frequency of initiating social grooming is a common occurrence. It is reasonable to assume the events are independent.

Frequency of initiating social grooming is a rare occurrence. It is reasonable to assume the events are dependent.

Frequency of initiating social grooming is a common occurrence. It is reasonable to assume the events are dependent.

Frequency of initiating social grooming is a rare occurrence. It is reasonable to assume the events are independent.

What is?

=

Write out the formula for the probability distribution of the random variabler.

P(r) =

(b) Find the probabilities that in your30minutes of observation, one otter will initiate social grooming four times, five times, and six times.

P(4) =

P(5) =

P(6) =

(c) Find the probability that one otter will initiate social grooming four or more times during the30-minute observation period.

(d) Find the probability that one otter will initiate social grooming less than four times during the30-minute observation period.