Start
here Wednesday
Poisson distribution
X =Number of "hits" in a fixed interval of
space or time (interval can be area or volume)
= Number of successes in
Binomial,
with p small and n large.
Lambda = np = expected number of
hits/successes
in the whole interval (whole n trials).
|___|_x_|___|___|__x|___|x__|___|
8 trials, 3 hits
Handout:
Tables
& stuff. Will go over the
proof
of the binomial~Poisson connection (handout, or p. 64) in class.
Note the table gives the probability < x, just like a Normal table.
HW Geometric:
Read Ash pp. 51-2. Also Finite
Geom. / Geometric Series, p. 36. HW Day
12
Read : Poisson Ash sec. 2-5, also p. 36,
the exponential series.
HW will be assigned Wed: Poisson Ash
p. 68, the non-Review problems:
#2
#3 (Poisson and binomial. compare)
4, 5, 6, 7
A. Suppose that on the average a certain
store gets 5 customers per hour. Consider now a two-hour period.
a) What is lambda for the 2-hour period?
b) What is the probability that the store
will
get 12 or fewer customers in the two hour period? (Use the table)
c) What is the probability that the store
will
get 13 or more customers in the two hour period?
d) What is the probability that the store
will
get exactly 13 customers in the two hour period?
B. Use Siegrist
Applet, Poisson Experiment.
Experiment: Number of arrivals in [0,t], r is the expected
number per unit time.
Lambda is shown as "mean", bottom of N column.
Do the Store of problem A, 2 hour period, 5
customers
per hour. (t=2, r=5) Run a few simulations.
Read off Distribution Table (right of graph) , Distribution column, the
probability
of 13 arrivals.
Compare with your answer to (Ad). It should
match, within .001.
Run r up and down, note the skewness of the
distribution
for small r, and the approach to normal for larger r.
The Geometric measured the waiting time
till
the first Binomial success.
There is a parallel variable measuring the
waiting time till the first Poisson hit. It's called the
Exponential,
but it's a continuous R.V. so we'll see it later.
- - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
| Sievers home | Math300-Sp04/Dayp13.htm | 8pm | 3/1/04 |