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.

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

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

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