Calculates the cumulative distribution function at a given evaluation point of a random variable within the table of random variables set.
3
, then this method will result the number of children with the nursery with an age less than or equal to three.The value of the distribution function in x
.
The random variables are defined on a discrete ordered set (i.e. a set which has a one-to-one mapping with a finite subset of integers) and so the cumulative distribution function of a given value is just the sum of the values of the random variables up to and including a given point.
Considering the experiment of counting the number of children of the ages 1, 2, 3, 4,
or 5
, within a nursery. Say the random variable f
, for this experiment is:
f(1) = 28
, i.e. the number of 1
year old children is 28
.
f(2) = 30
, i.e. the number of 2
year old children is 30
.
f(3) = 26
, i.e. the number of 3
year old children is 26
.
f(4) = 32
, i.e. the number of 4
year old children is 32
.
f(5) = 30
, i.e. the number of 5
year old children is 30
.
Then the associated cumulative random variables g
, takes the values:
g(1) = f(1) = 28
, i.e the number of children of age 1
.
g(1) = f(1) + f(2) = 28 + 30
, i.e the number of children of 2
years old or younger.
g(1) = f(1) + f(2) + f(3) = 28 + 30 + 26
, i.e the number of children of 3
years old or younger.
g(1) = f(1) + f(2) + f(3) + f(4) = 28 + 30 + 26 + 32
, i.e the number of children of 4
years old or younger.
g(1) = f(1) + f(2) + f(3) + f(4) + f(5) = 28 + 30 + 26 + 32 + 30
, i.e the number of children of 5
years old or younger.
In order to apply this method to the study of random variables you will first need to set the random variables within the internal table (i.e. an ordered collection of random variables) by using one or more of the following:
i
th position within the random variable table.
Note: If one of the random variables is either incorrectly set or is no longer in use then it can be removed from the table using (int).
RandomVariables Class | DiscreteProbability Namespace