Question

A robot is programmed to build cars on a production line. The robot breaks down at random at a rate of once every 24 hours.

(a) [5 Points] Find the probability that it will work continuously for 48 hours without a breakdown.

(b) [5 Points] Find the probability that, in an 24 hour period,1 the robot will break down at least once,

(c) [5 Points] Find the probability that, in an 24 hour period, there are exactly 2 breakdowns

Answer 1

µ = 1 per 24 hours

This is a poisson distribution

P(X = x) = e^-µ * µ^x / x!

a) µ = 2 per 48 hours

P(X = 0) = e^-2 * 2⁰ / 0! = 0.1353

b) µ = 1 per 24 hours

P(X > 1) = 1 - P(X = 0)

              = 1 - e^-1 * 1⁰ / 0!

              = 1 - 0.3679

              = 0.6321

c) P(X = 2) = e^-1 * 1² / 2! = 0.1839