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Notes › EENG 3421: Probability and Statistics for Engineers Lecture 15

More on Cumulative Distribution Function

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CDF

Definition 15.1 (Cumulative Distribution Function).

The cumulative distribution function of random variable $X$ is

$$ F_X(x)=P[X\le x] $$
Theorem 15.2 (CDF Boundary Values and Interval Probability).

For any random variable $X$

$$ F_X(-\infty)=0 $$$$ F_X(\infty)=1 $$

For $x_1 $$ P[x_1

Definition 15.3 (Continuous Random Variable).

$X$ is a continuous random variable if the CDF $F_X(x)$ is a continuous function

Corollary 15.4 (Upper Tail From CDF).

For any real number $a$

$$ P[X>a]=1-F_X(a) $$

References

  • Course lecture slides 18–20

Sources

  • Course lecture slides 18–20

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