Question

In analyzing hits by certain bombs in a​ war, an area was partitioned into 582 regions, each with an area of 0.85 km².  A total of 525 bombs hit the combined area of 582 regions. Assume that we want to find the probability that a randomly selected region had exactly two hits. In applying the Poisson probability distribution​ formula, $LaTeX: P\left(x\right)=\frac{\lambda^x\:\bullet\:\:e\:^{-\lambda}}{x!}$ P ( x ) = λ x ∙ e − λ x !, identify the values of $LaTeX: \lambda,\:x,\:and\:e.$ λ , x , a n d e . Also, briefly describe the values of $LaTeX: \lambda,\:x,\:and\:e.$ λ , x , a n d e .(​Type integers or decimals rounded to five decimal places as​ needed.)

Briefly describe what the symbol $LaTeX: \lambda$ λ represents.

Briefly describe what the symbol x represents.

Briefly describe what the symbol e represents.

Answer 1

$\lambda$ = 525/582 = 0.90206

x = 2

e = 2.61828 (base of the natural logarithm)

The probability that a randomly selected region had exactly two hits

= P(X = 2)

= = 0.1651

-0.90206 * 0.902062

Symbol $\lambda$ represents average number of bombs hit in a randomly selected region

Symbol x represents the number of bombs for which the probability needs to be found out

Symbol e is a fixed constant which is base of the natural logarithm