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}

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