A company makes certain device. We are interested in lifetime of the device. It is determined that around 2% of the devices are defective from start so they've the lifetime of 0 years. If the device isn't defective, then the lifetime of device is exponentially distributed with the parameter lamda=2 years. Let X be the lifetime of randomly selected device.
a.) Determine the generalized PDF of X.
b.) Determine P(X>or equal to 1).
c.) Determine P(X>2|X>or equal to 1).
d.) Determine EX and Var(X).