Mathematics · Ch 11 — Probability Distributions

Distribution function from Probability density function

11.4.4

Distribution function from Probability density function

Both $f$ and $F$ carry the full probability information of a continuous $X$ , and either determines the other. Given the pdf $f(x)$ , the cdf is built by integrating piece by piece over each interval on which $f$ has a different formula, always starting the accumulation from $-\infty$ :

$F(x)=\int_{-\infty}^{x} f(u)\,du.$ …

Figure 11.16Triangular probability density function: f(x) = x - 1 on 1 <= x < 2 rising to a peak of 1 at x = 2, then f(x) = -x + 3 on 2 <= x < 3 falling back to 0 at x = 3

Fig. 11.16 — Triangular probability density function: f(x) = x - 1 on 1 <= x < 2 rising to a peak of 1 at x = 2, then f(x) = -x + 3 on 2 <= x < 3 falling back to 0 at x = 3

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your textbook's own diagram.

What this figure shows. Triangular probability density function: f(x) = x - 1 on 1 <= x < 2 rising to a peak of 1 at x = 2, then f(x) = -x + 3 on 2 <= x < 3 falling back …

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