The life span X in years of a device is distributed according to the following density:

The manufacturer gives a warranty of 6 months. When the device fails within these 6 months he will take the old device back and provides a new one. The warranty is not renewed.

a. Check whether f is indeed a density.

b. Determine the probability that a device fails within the warranty period of 6 months.

c. Determine the expected value of the profit per sold device if the manufacturer sells the devices for 90 euro, while producing a device costs him 50 euro.

Transcribed Image Text:

f(x) = 4-x 8 0, 0≤x≤4 elsewhere f(x) = 4-x 8 0, 0≤x≤4 elsewhere