Homework 4

Spatial Analysis, Spring 2001

Due Feb 12 2001

1.

You are an agricultural extension officer for a rural area in Tanga, Tanzania. Many of the farmers in your region grow cardamon as a cash crop. You have been receiving reports of a blight in your district, averaging two new cases per day. For the last three days, not a single new report of a case of blight has been reported. You hope that the epidemic is over or slowing down, but you can't be sure. What is the probability, if the epidemic is going on at its same rate, that you would have three days with no new cases reported?

2.

This kind of blight is new, and noone really knows how it is transmitted from one grove to an other. Your first clue to how it is transmitted from tree to tree might be the spatial concentration of cases; if it is transmitted through the air, you might expect that the cases would be concentrated in a single area. If they are transmitted through something else (birds, direct inoculation, or something else), you might suspect that they are more random. You map out cases in an area of prime cardamom growing land, and divide it up into square kilometer plots. The map produced looks like thus:

(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?

(c)

Based on a qualitative 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?