Cumulative Distribution Function - Examples

Examples

As an example, suppose X is uniformly distributed on the unit interval . Then the CDF of X is given by

F(x) = \begin{cases} 0 &:\ x < 0\\ x &:\ 0 \le x < 1\\ 1 &:\ 1 \le x. \end{cases}

Suppose instead that X takes only the discrete values 0 and 1, with equal probability. Then the CDF of X is given by

F(x) = \begin{cases} 0 &:\ x < 0\\ 1/2 &:\ 0 \le x < 1\\ 1 &:\ 1 \le x. \end{cases}

Read more about this topic:  Cumulative Distribution Function

Famous quotes containing the word examples:

    “There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
    —Bernard Mandeville (1670–1733)

    “Histories are more full of examples of the fidelity of dogs than of friends.”
    —Alexander Pope (1688–1744)

    “No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
    —André Breton (1896–1966)