The First Pass worksheet
computes first passage probabilities from a given initial
state to some other state. In the case shown, the first passage
probabilities from state 0 to state 1 are shown in the last
column of the display. The Start button allows entry
of the initial and final states. The More button computes
more first passage probabilities in sets of 20 (the number
is set when the page is first created).
This display is showing the probability
distribution for the number of months required to pass from
a new bulb to a bulb one month old for the first time.
For the bulb example, the probability of first passage in
one month is 0.5, the probability that the bulb does not fail
during the first month. To have a first passage time of two
months, the bulb must fail in the first month, but not fail
in the second. This result has a probability of 0.25. For
this simple case, the first passage probabilities are simply
the geometric distribution with p = 0.5. The worksheet
also shows the expected first passage times from each state
into the specified final state. This vector is shown in the
display at the right.