Question

assume that each of 2000 frogss living near a nuclear power plant is exposed to particles of a certain kind of radiation at an average rate of one per week. suppose that each hit by a particle is harmless with probability 1 - 10-5 , and produces a tumor with probability 10-5 . find the approximate distribution of

Answer 1

distribution of the total number of tumors produced in the whole population over a one-year period by this kind of radiation is 0, 1, 2, ..................104000.

let, x denote the total number of hits,

y denotes the number of hits by a particle in a year or an individual,

one per week ⇒ 52 per year

therefore, rate = 52 per year

since it is very rare to hit all individuals, we can use Poisson distribution.

therefore by using the formula p (x = x) = (e^(-rate) × rateˣ) ÷ x! ; x = 0, 1, 2, ............( 2000 × 52)

p (x = 2) = (e⁻⁵² × 52ˣ) ÷ x! ; x = 0, 1, 2, ............104000

now each hit has a harm of probability 10⁻⁵.

so p(total no. of tumors produced over a one year period)

= {e⁻⁵² × 52ˣ} ÷ x! × 10⁻⁵ ; x = 0, 1, 2, ............104000

therefore total no. of tumors = 2000 × (e⁻⁵² × $52^{x.10^{-5} }$ ) ÷ x!  × xⁿ ; x = 0, 1, 2, ............104000

Know more about Poisson distribution here: brainly.com/question/17280826

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(complete question)

Assume that each of the 2000 individuals living near a nuclear power plant is exposed to particles of a certain kind of radiation at an average rate of one per week. Suppose that each hit by a particle is harmless with a probability of 1 - 10⁻⁵, and produces a tumor with a probability of 10⁻⁵. Find the approximate distribution of the total number of tumors produced in the whole population over a one-year period by this kind of radiation.