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