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The length of life Y for fuses of a certain type is modeled by the exponential distribution, with (please view the attachment for the expression)

a. If two such fuses have independent lengths of life Y_1 and Y_2, find the joint pdf for Y_1 and Y_2.

b. One fuse in part (a) is in a primary system and the other is in a backup system that come into use only if the primary system fails. The total effective length of life of the two fuses is then Y_1 + Y_2. Find P(Y_1 + Y_2 </= 1).

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A joint PDF in a solver is determined for an exponential distribution model.

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