Binomial Probability Presentation
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1Binomial Probability Presentation
Poisson Probability Presentation
X=# of (successes)
X=# of (successes) IN (time of space)
n= ____________
λ= (given rate)
Π= (decimals)
P (
) = P (X symbol #) = Ppd or Pcd (X, λ) = 0.xxxx
P (
) = P (X symbol #) = Bpd or Bcd (X, n, Π) = 0.xxxx
(words)
(<,>,≤, ≥,=)
(4decimals)
(words)
(<,>,≤, ≥,=)
(4decimals)
•If (=) then Ppd
•If (=) then Bpd
•If (>) then Pcd, but for example (X>5 means 1-X≤5). This is when
•If (>) then Bcd, but for example (X>5 means 1-X≤5). This is when
they ask a more than type question.
•If (<) then Pcd, but for example (X<5 means X≤4). This is when
they ask a more than type question.
•If (<) then Bcd, but for example (X<5 means X≤4). This is when
they ask a less than type question.
•If (≤) then Pcd. This is when they ask an at most type question.
they ask a less than type question.
•If (≤) then Bcd. This is when they ask an at most type question.
•If (≥) then Pcd, but for example (X≥5 means 1-X≤5). This is when
•If (≥) then Bcd, but for example (X≥5 means 1-X≤5). This is when
they ask an at least type question.
they ask an at least type question.
Characteristics
Characteristics
The main feature of Poisson probabilities is space and time. In
The key feature of Binomial probabilities is that each trial during
Poisson probabilities you are inspecting or analyzing the amount
the experiment will result in 2 outcomes. One is a success (what
of space. This could be classified as length, area, volume, or
your interested in), and the other is a failure. These outcomes
weight. Also the experiment conducted is observation based that
could be ‘characteristics’ that make them either a success or
situates in a period of time.
failure such as getting a head or tails, rolling a 5 on a die, …etc.
If time or space was collapsed into something immeasurable you
Another attribute of Binomial distributions is that you are
can assume there is going to be a success or no success (successes
experimenting with ‘n’ trials or repetitions of an action such as
is the outcome of interest). Also successes must occur randomly.
flipping a coin or you have selected a sample of ‘n’ items from a
Therefore successes are independent of each other.
large population.
In this distribution we denote the average success rate of the
Successes = п
amount of time or space we are interested in as the symbol λ
Failures = (1-п)
(Lambda).
Therefore, the trials are independent of each other.
Binomial Probability Distribution Function.
Poisson Probability Distribution Function.
Bpd and Ppd can be calculated
manually with these functions,
e=2.718281828459… (a mathematical constant)
whereas Bcd a Pcd could be
P(X = x) =
n!
calculated manually but are
more complex to, since they are
п
(1-п)
n-x
P(X = x) = e
-λ
λ
x
x
cumulative type probabilities.
x!(n-x)!
x!
By: Sulosan
Thangarajah
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