Question
Consider two components whose lifetimes X, and
X2 are independent and exponentially distributed
with parameters à, and 22, respectively. Obtain
the joint pdf of total lifetime X, + X2 and the
proportion of total lifetime X/(X, + X2) during
which the first component operates.
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Transcribed Image Text

Consider two components whose lifetimes X, and X2 are independent and exponentially distributed with parameters à, and 22, respectively. Obtain the joint pdf of total lifetime X, + X2 and the proportion of total lifetime X/(X, + X2) during which the first component operates.

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