contestada

Benford's Law states that the probability that the first decimal-digit of a raw data sample (from 1 to 9) is given
Pm = log (m +1) - log m. That is, about (100P)% of the data can be expected to have m as the first digit. Complete parts a and b below.
a. What percent of the data can be expected to have 4 as the first digit?
Pa =
(Round to three decimal places as needed.)
b. Find P1+P2 + ... + P9. Interpret your result.
Py + P2 + ... +P9 =
(Type an integer or a decimal.)​

Respuesta :

tramserran

Answer:  P(4) = 0.097

                [tex]\bold{\sum_{m=1}^9=1}[/tex]

Step-by-step explanation:

[tex]P(m)=\log(m+1)-\log(m)\\\\.\qquad =\log\bigg(\dfrac{m+1}{m}\bigg)\qquad \text{(using rules for condensing logs)}\\\\\\P(4)=\log\bigg(\dfrac{4+1}{4}\bigg)\\\\\\.\qquad =\log\bigg(\dfrac{5}{4}\bigg)\\\\\\.\qquad =\large\boxed{0.097}[/tex]

[tex]\sum_{m=1}^9\log\bigg(\dfrac{m+1}{m}\bigg)\\\\\\.\qquad =\log\bigg(\dfrac{2}{1}\bigg)+\log\bigg(\dfrac{3}{2}\bigg)+...\log\bigg(\dfrac{9}{8}\bigg)+\log\bigg(\dfrac{10}{9}\bigg)\\\\\\.\qquad =\log\bigg(\dfrac{2}{1}\bigg)\bigg(\dfrac{3}{2}\bigg)...\bigg(\dfrac{9}{8}\bigg)\bigg(\dfrac{10}{9}\bigg)\qquad \text{(using rules for condensing logs)}\\\\\\.\qquad =\log\bigg(\dfrac{10!}{9!}\bigg)\\\\\\.\qquad =\log(10)\\\\\\.\qquad =\large\boxed{1}[/tex]

Otras preguntas