A company makes a certain device. We are interested in the lifetime of the device. It is estimated that around 2% of the devices are defective from the start so they have a lifetime of 0 years. If a device is not defective, then the lifetime of the device is exponentially distributed with a parameter lambda = 2 years. Let X be the lifetime of a randomly chosen device.
a. Find the PDF of X.
b. Find P(X greaterthanorequalto 1).
c. Find P(X > 2|X greaterthanorequalto 1).
d. Find E(X) and Var(X).
