mathematical problem

Suppose a weather-reporting station has an electronic wind speed monitor whose time to failure is known to follow an exponential model1?e?1/?, 0 < ? < ?.Let Y1 be the time until the monitor fails to work. The station also has a backup monitor; let Y2 be the time until this second monitor fails. Thus, the time Y until the monitoring is out of commission is the sum of two independent exponential random variables, Y1 and Y2. Thus Y =Y1 +Y2 hasagammapdf,sofY(y;?)= 1ye?y/?, 0?y