Electronic components of a certain type have a length of life
Y
, with probability density given by
f(y)={ (1/100)e −y/100
,
0,
​
y>0
elsewhere ​
(Length of life is measured in hours.) (a) Suppose that two such components operate independently and in series in a certain system (hence, the system fails when either component fails.) Find the density function for
X
, the length of life of the system. (b) Suppose that the components operate in parallel (hence, the system does not fail until both components fail). Find the density function for
X
, the length of life of the system.