Answer to Question #215882 in Statistics and Probability for Math

Question

let the continuous random variable x denote the current measured in a thin copper wire in milliamperes. The probability density function is given by

Answer 1

$f(x)=\dfrac{1}{20}, for\ 0\leq x\leq 20$

1.

$P(5<X<10)=\displaystyle\int_{5}^{10}\dfrac{1}{20}dx=[\dfrac{1}{20}x]\begin{matrix} 10 \\ 5 \end{matrix}$

$=\dfrac{10}{20}-\dfrac{5}{20}=\dfrac{1}{4}$

2. Using Uniform distribution

$F(x)=\dfrac{x-0}{20-0}$

$P(5<X<10)=F(10)-F(5)$

$=\dfrac{10-0}{20-0}-\dfrac{5-0}{20-0}=\dfrac{1}{4}$

3.

$\mu=\dfrac{A+B}{2}=\dfrac{0+20}{2}=10$

$\sigma^2=\dfrac{(B-A)^2}{12}=\dfrac{(20-0)^2}{12}=\dfrac{100}{3}$

$\sigma=\sqrt{\sigma^2}=\dfrac{10\sqrt{3}}{3}$