Question

Notation In analyzing hits by V-1 buzz bombs in World War II, South London was partitioned into 576 regions, each with an area of 0.25 \(k{m^2}\) . A total of 535 bombs hit the combined area of 576 regions. Assume that we want to find the probability that a randomly selected region had exactly two hits. In applying Formula 5-9, identify the values of \(\mu \), x, and e. Also, briefly describe what each of those symbols represents.

Short answer

\(\mu \)denotes the mean number of bomb hits per region. Its value is equal to 0.929.

x denotes the number of hits required to compute the desired probability. Its value is equal to 2.

e denotes the constant in the Poisson probability formula. Its value is approximately equal to 2.71828.

Step-by-step solution

Given information

It is given that a total of 535 bomb hits the area of South London with 576 regions.

Identify the values and the meaning of symbols\(\mu \), x, and e

The mean number of hits per region is denoted by\(\mu \).

The value of\(\mu \)is computed below:

\(\begin{array}{c}\mu = \frac{{{\rm{Number}}\;{\rm{of}}\;{\rm{bomb}}\;{\rm{hits}}}}{{{\rm{Number}}\;{\rm{of}}\;{\rm{regions}}}}\\ = \frac{{535}}{{576}}\\ = 0.929\end{array}\)

Thus,\(\mu = 0.929\).

The number of hits required to compute the probability is denoted by x.

Here, x=2.

e is the constant that is used in the Poisson probability formula. It is also called the Euler’s number.

The value of e is approximately equal to 2.71828.