Harvard statistics, video 11 note(Poisson Distribution)
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7:39 2014-10-11 Saturday
start Harvard statistics, video 11
the Poisson distribution
7:39 2014-10-11
sympathetic magic:
don't confuse r.v. with its distribution
7:46 2014-10-11
"word is not the thing, map is not the territory"
7:48 2014-10-11
the r.v. is a house,
the distributuion is a blue print
7:51 2014-10-11
Poisson distribution
7:54 2014-10-11
rate parameter
7:57 2014-10-11
1st let's check this is a valid PMF
7:57 2014-10-11
X ~ Pois(λ)
8:00 2014-10-11
often used for the application where
counting the #of successes, where we have a large
number of trials, each one with a small probability
of success
* #emails receive per hour
8:06 2014-10-11
we have a large number of things that could happen,
but each one is unlikely // Poisson distribution
8:12 2014-10-11
weakly dependent
8:12 2014-10-11
Poisson Paradigm(Poisson Approximation)
8:15 2014-10-11
Bernoulli(p)
8:16 2014-10-11
we can prove Binomial(n, p) does converge to Poisson
when n gets large & p gets small
8:16 2014-10-11
Binomial => Poisson // Binomial converges to Poisson
8:32 2014-10-11
create a indicator r.v.
8:41 2014-10-11
now we're going to use the "Poisson Approximation"
start Harvard statistics, video 11
the Poisson distribution
7:39 2014-10-11
sympathetic magic:
don't confuse r.v. with its distribution
7:46 2014-10-11
"word is not the thing, map is not the territory"
7:48 2014-10-11
the r.v. is a house,
the distributuion is a blue print
7:51 2014-10-11
Poisson distribution
7:54 2014-10-11
rate parameter
7:57 2014-10-11
1st let's check this is a valid PMF
7:57 2014-10-11
X ~ Pois(λ)
8:00 2014-10-11
often used for the application where
counting the #of successes, where we have a large
number of trials, each one with a small probability
of success
* #emails receive per hour
8:06 2014-10-11
we have a large number of things that could happen,
but each one is unlikely // Poisson distribution
8:12 2014-10-11
weakly dependent
8:12 2014-10-11
Poisson Paradigm(Poisson Approximation)
8:15 2014-10-11
Bernoulli(p)
8:16 2014-10-11
we can prove Binomial(n, p) does converge to Poisson
when n gets large & p gets small
8:16 2014-10-11
Binomial => Poisson // Binomial converges to Poisson
8:32 2014-10-11
create a indicator r.v.
8:41 2014-10-11
now we're going to use the "Poisson Approximation"
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