Find the value of c which will make the function a pdf on the interval .

Question

Find the value of c which will make the function  a pdf on the interval  .

Quizplus · Accepted Answer

To be a probability density function (pdf), the integral of the function over its entire domain must equal to 1. In this case, we need to solve for c such that:

∫exp(-x/6)dx from 11 to 17 = 1

Using integration by parts, we get:

-6exp(-x/6) from 11 to 17 = 1

-6(exp(-17/6) - exp(-11/6) = 1

-6(0.116 - 0.262) = 1

c = 1/[6(0.146)] = 0.452

Therefore, the answer is option C.

Find the Value of C Which Will Make the Function