Question

Estimate the probability that X>1,200 particle /m

2
when λ=1000 particles /m
2
in a Poisson process. P(x>1,200) fonn

Answer 1

To estimate the probability that X>1,200 particle/m² when λ=1000 particles/m² in a Poisson process, use the Poisson distribution and complementary probability.

Step-by-step explanation:

To estimate the probability that X>1,200 particle/m² when λ=1000 particles/m² in a Poisson process, we can use the Poisson distribution. In this case, X follows a Poisson distribution with a mean of λ=1000. To find the probability that X>1,200, we can use the complementary probability, which is 1 minus the cumulative distribution function (CDF) of X up to 1,200. First, find the CDF of X up to 1,200 using the poissoncdf(1000, 1200) function, which will give you a value of approximately 0.9726. Then, subtract this value from 1 to find the probability that X>1,200, which is approximately 0.0274 or 2.74%