Problem 13BSC

Use the Poisson distribution to find the indicated probabilities.

World War II Bombs In Exercise we noted that in analyzing hits by V-l buzz bombs in World War II, South London was partitioned into 576 regions, each with an area of 0.25 km2. A total of 535 bombs hit the combined area of 576 regions.

a. Find the probability that a randomly selected region had exactly 2 hits.

b. Among the 576 regions, find the expected number of regions with exactly 2 hits.

c. How does the result from part (b) compare to this actual result: There were 93 regions that had exactly 2 hits?

Exercise

Notation In analyzing hits by V-l buzz bombs in World War II, South London was partitioned into 576 regions, each with an area of 0.25 km2. 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 µ, x, and e. Also, briefly describe what each of those symbols represents.

Problem 13BSC

Answer:

Step1 of 1:

We have In Exercise we noted that in analyzing hits by V-l buzz bombs in World War II, South London was partitioned into 576 regions, each with an area of 0.25 km2. A total of 535 bombs hit the combined area of 576 regions.

Consider a random variable “x” follows poisson distribution with sample size “n” and parameter “”.

i,e.X P()

Probability mass function of poisson distribution is given by

P(x) = , x = 0,1,2,...,n.

Where, e = 2.71828.

And .

a).

The probability that a randomly selected region had exactly 2 hits is given by P(x = 0) = ?

Consider,

P(x) =

P(x = 2) =

=

= 0.1703.

b).

The expected number of regions with exactly 2 hits is given by E(x) = nP(x = 2)

= 5760.1703

= 98.1500.

c).

The expected number of regions with exactly 2 hits is close to 93, which is these actual number of region with 2.