Suppose that trees are distributed in a forest according to a two-dimensional Poisson process with parameter α, the expected number of trees per acre, equal to 80.a. What is the probability that in a certain quarter-acre plot, there will be at most 16 trees?b. If the forest covers 85.000 acres, what is the expected number of trees in the forest?c. Suppose you select a point in the forest and construct a circle of radius .1 mile. Let X = the number of trees within that circular region. What is the pmf of X? [Hint: 1 sq mile = 640 acres.)
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Suppose that trees are distributed in a forest according to a two-dimensional Poisson process with parameter α, the expected number of trees per acre, equal to 80.
a. What is the probability that in a certain quarter-acre plot, there will be at most 16 trees?
b. If the forest covers 85.000 acres, what is the expected number of trees in the forest?
c. Suppose you select a point in the forest and construct a circle of radius .1 mile. Let X = the number of trees within that circular region. What is the pmf of X? [Hint: 1 sq mile = 640 acres.)
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