If the pdf of a curve X is
`f(x)={{:(k.e^(-thetax)","thetagt0","0lexltoo),(0","ooltxlt0" then k is equal to"):}`

Options

A. 1
B. `theta/2`
C. `theta`
D. `2theta`

Answer

C

Explanation

`thereforef(x)` is the pdf
`therefore" "oversetoounderset(-oo)intf(x)dx=1rArroversetoounderset0intk.e^(-thetax)dx=1`
`rArr" "k[e^(-thetax)/(-theta)]_0^oo=1`
`rArr" "=k/theta[1/e^(thetax)]_0^oo=1`
`rArr" "-k/theta[1/e^oo-1/e^0]=1`
`rArr" "-k/theta[1/oo-1/1]=1`
`rArr" "-k/theta[0-1]=1rArrk/theta=1`
`therefore" "k=theta`