Question

If pdf of a curve X is `f(x)=ae^(-ax),xge0,agt0`
If `P(0ltXltK)=0.5` , then the k is equal to
A. `1/8`
B. `1/alog2`
C. `1/2log2`
D. `1/aloga`

Answer 1

Correct Answer - B
Given `P(0ltXltK)=0.5`
`oversetKunderset0intf(x)dx=1/2rArroversetKunderset0intae^(-ax)dx=1/2`
`rArr" "a[e^(-ax)/(-a)]_0^K=1/2rArr-[e^(-ax)]_0^K=1/2`
`rArr" "-(e^(-aK)-e^0)=1/2rArr-e^(-aK)+1=1/2`
`rArr" "e^(-aK)=1/2rArr-ak=log(1/2)`
`rArr" "aK=log2rArrK=1/alog2`