Following is the probability density function `f(x)=pxe^(-4x^2),0lexleoo` . Then the value of p is

Options

A. 8
B. 5
C. 7
D. -1

Answer

A

Explanation

`oversetoounderset0intf(x)dx=1`
`rArr" "oversetoounderset0intpxe^(-4x^2)dx=1rArrp[e^(-4x^2)/(-8)]_0^oo=1`
`[{:(therefore"put"-4x^2=trArrxdx=(dt)/(-8)),(thereforeinte^t(dt)/(-8)=e^t/(-8)=e^(-4x^2)/(-8)):}]`
`rArr" "(-p)/8[1/e^(4x^2)]_0^oo=1rArr(-p)/8[1/oo-1/1]=1`
`rArr" "p/8=1rArrp=8`