Question

Introduction to Poisson and Exponential distribution, Memoryless Property

You are working to statistically model the location of defects on the surface of a 3D printed material. After analyzing for one month you found out that the number of defects in the material follows a Poisson process, with an average of one defect is found every 10µm² area. One of your lab mates is willing to validate the information. He selects 60 µm² are on the surface to study the location of defects. Using this information provided, answer question 1.

1. What is the probability that your lab mate finds at least 4 defects on the surface area he is observing (round to 3 digits)?

Answer 1

lambda = 6

P(X >= 4)
= 1 - P(X <= 3)
= 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) )
= 1 - (e^-6 + e^-6*6^1 + e^-6*6^2/2! + e^-6*6^3/3!)
= 0.8488

Ans: 0.849