The lifetimes (in months) of two types of lightbulbs are independent Exponential variables with means $1/1.20$ and $1/0.55$ respectively.

Part a)
Consider the total lifetime of the two bulbs used consecutively in a light fitting, so that when the first bulb expires it is immediately replaced by one of the second type. Evaluate the density function of this variable at the point $2.65$, giving your answer to two decimal places.


Part b)
If the mean lifetimes were equal, the total lifetime in (a) follows which type of distribution?

A. Poisson
B. Normal
C. Exponential
D. Gamma
E. Uniform