Extensive analysis of time (in years) till major breakdown of popular brand of motorcycle shows that it follows hazard function λ(t) = .4 + .3t
Remembering that hazard function can be interpreted as quick manner to determine how likely short-term failure is, P=λ(t)Δt , compute (approximately) the probability that motorcycle that has run flawlessly for 15 months will have major breakdown in the next week.
This brand of motorcycle has a 2-year warranty. Find out the probability that new cycle will have a major breakdown before the warranty expires.