In: Math
An 10-bit password is required to access a system. A hacker systematically works through all possible 10-bit patterns. Let ? be the number of patterns tested until the correct password is found.
(a) Find ?? and the pmf of ?.
Let ? be the event that the password has not been found after 24 tries.
(b) Find the conditional pmf of ? given ?.
(c) Find ?(?) and ?(? | ?).