An electronics gadget company has currently created new line of fitness devices that monitor individual's activity during the day. The lifetime of device is distributed exponentially with expected life time of 430 days. Once activated, the device is always upon and is to be worn at all times.
a) Describe cumulative density function, F(X)=P(X
b) Determine the probability that a randomly chosen device will have a lifetime greater than two years?
c) Assume a group of 5 friends each buy a new fitness device. Determine the probability that 4 or more of the devices will have a lifetime greater than two years?