Problem $3$: You need to download two files: file $1$ and file $2.$ File $1$ is available via

source A or source B$.$ File $2$ is available only via source C$.$ The time to download file $1$

from source A is exponentially distributed with rate $1.$ The time to download file $1$ from

source B is exponentially distributed with rate $2.$ The time to download file $2$ from source

C is exponentially distributed with rate $3.$ You decide to download from all three sources

simultaneously, in the hope that you get both file $1$ and file $2$ as soon as possible. Let T

denote the time until you get both files.

$($a$)$ What is E$[$T$]?$

$($b$)$ What is P$($T $<$ t$)?$