Please help me with my homework assignment:

Q4a:

Consider a Bernoulli process, with arrival probability at each

time slot equal to=1/3.

An observer arrives at time slot 10 and sees that no arrival

took place in that slot. A passerby informs the observer that there was exactly

one arrival during the preceding two time slots (i.e., time slots 8 and 9) but

has no additional information about which of the two it was.

Letbe the

number of time slots starting from the time slot of the last arrival (before

slot 10) and until the time slot where the next arrival comes.

For example, if the last arrival came at time 8 and the next

arrival comes at time 13,

is the

number of slots in the interval{8,9,10,11,12,13}, so that=6.

(Enter a numerical expression or a decimal accurate to at least

3 decimals places.)

Find the probability that=4.

Q4b:

Continue from and use the same setup as above.

Find the expected value of.