ASSIGNMENT 7 PS2

IS 605 FUNDAMENTALS OF COMPUTATIONAL MATHEMATICS

Your organization owns a copier (future lawyers, etc.) or MRI (future doctors). This machine has a manufacturer’s expected lifetime of 10 years. This means that we expect one failure every ten years. (Include the probability statements and R Code for each part.).

  1. What is the probability that the machine will fail after 8 years?. Provide also the expected value and standard deviation. Model as a geometric. (Hint: the probability is equivalent to not failing during the first 8 years..)
#Probability
round(pgeom(8, .1, lower.tail = FALSE),2)
## [1] 0.39
#Expected value
1/.1
## [1] 10
#Standard deviation
round(sqrt((1-.1)/(.1^2)),2)
## [1] 9.49
  1. What is the probability that the machine will fail after 8 years?. Provide also the expected value and standard deviation. Model as an exponential.
#Probability
round(pexp(8, .1, lower.tail = FALSE),2)
## [1] 0.45
#Expected value
1/.1
## [1] 10
#Standard deviation
round(sqrt((1-.1)/(.1^2)),2)
## [1] 9.49
  1. What is the probability that the machine will fail after 8 years?. Provide also the expected value and standard deviation. Model as a binomial. (Hint: 0 success in 8 years)
#Probability
round(pbinom(0, 8, .1 ),2)
## [1] 0.43
#Expected value
.1*8
## [1] 0.8
#Standard deviation
round(sqrt(8*.1*(1 - .1)),2)
## [1] 0.85
  1. What is the probability that the machine will fail after 8 years?. Provide also the expected value and standard deviation. Model as a Poisson.
#Probability
round(pexp(8, .1, lower.tail = FALSE),2)
## [1] 0.45
#Expected value
.1*8
## [1] 0.8
#Standard deviation
round(sqrt(8*.1),2)
## [1] 0.89