Originally Posted by

**oxrigby** Hi I was given this question in an exam and unfortunately didnt know how to do it obtaining zero out of seven.

A continuous random variable, X, had density function of the form

$\displaystyle f(x)=\left( \begin{array}{cc}0, & \mbox{ if } x<1\\a+\frac{b}{x^4}, & \mbox{ if } x>1\end{array}\right)$

where a and b are constants(i) calculate the values of a and b.

I figured since the integral of the density function from $\displaystyle -\infty$ to $\displaystyle +\infty$ is 1, a and b could be derived but i don't get anywhere.

here is my working:-

$\displaystyle \int_1^\infty(a+\frac{b}{x^4})dx=a\int_1^\infty(1) dx+b\int_1^\infty(x^-4)dx$ which gives me $\displaystyle a(\infty-1)+b(-\frac{1}{\infty}-\frac{1}{3})=1$ Im not exactly sure but i think this gives me roughly ab=1,,,do i just sub then for instance $\displaystyle a=\frac{1}{b}$back into my original integral??? im not sure as this gives me $\displaystyle b=\infty$

If anyone could give me some idea as to how I could get a reasonable or solid answer you'll be very helpful!!!