Homework 9

Spatial Analysis, Spring 2001

Due April 23 2001

1.

We are revisiting the blight case in homework 4. You have calculated the likelyhood of blight occuring on a grid in that homework assignment. Now, you are asked to determine if this represents a truly random distribution of blight cases. Can you find evidence that this distribution of points is not randomly distributed?

(a)

If the spatial distribution of blight cases were random, how would you expect to see the blight cases distributed between cells (for example, how many cells with no blight, how many with one case of blight, etc.)? (hint: $P(x) = \frac{e^{-\lambda}\lambda^x}{x!}$)

(b)

What is the allocation in that you observe in the present setup?

(new question:)

(c)

Based on a quantitative comparison of the allocations, would you say that the points are randomly distributed? Is this the same conclusion that you would have by simply looking at the map?

2.

You discover that the parasite that is causing the infection in this area has a seed sack that ``pops'' (ejects spores) after a certain gestation period. You measure the gestation time for the ejections on a few plants, and get the following numbers:

gestation time (days)

7

9

3

9

7

4

4

6

It's suggested that the gestation time is normally distributed.

(a)

Calculate the summary statistics ( $\mu, \sigma, n$) for the data set.

(b)

Show quantitatively that the data are or are not normally distributed (as always, state hypothesis, show calculations, state conclusions).

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Homework 9

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