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in a study, we found that there are 1000 particles of dust in each squared meter....

in a study, we found that there are 1000 particles of dust in each squared meter. Calculate the probability that: A) we find 1100 particles in 1 squared meter. B) 550 particles in 1/2 squared meter

Math   Statistics-And-Probability   
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Answer #1

Let X denotes the number of particles in 1 squared meter.

X ~ Poisson(1000)

The probability mass function of X is

Now,

a) The probability that there are 1100 particles in 1 squared meter

Let Y denotes the the number of particles in 1/2 squared meter.

Y~ Poisson(500)

The probability mass function of Y is

Now,

b) The probability that there are 550 particles in 1/2 squared meter

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