Answer to Question #141707 in Statistics and Probability for onkar kolhe

Question

Suppose that the battery failure time. measured in hours, has a probability density
function given by:

f(x) =2/(x+1)), x>=0

The probability that the battery lasts longer than five hours is:

Answer 1

Suppose that the battery failure time. measured in hours, has a probability density

function given by:

$$f(x) = \begin{cases} \dfrac{2}{(x+1)^3}, x\geq 0 \\ \ \ \ \ \ \ \ 0 \ \ \ \ \ \ \ \ x<0 \end{cases}$$

$$P(X>5)=1-P(X≤5)=1-\displaystyle\int_{0}^5\dfrac{2}{(x+1)^3}dx=$$

$$=1-\big[-\dfrac{1}{(x+1)^2}\big]\begin{matrix} 5 \\ 0 \end{matrix}=1+\dfrac{1}{36}-1=\dfrac{1}{36}$$