Question

How do I find B so that f(x) is a continuous RV pdf?

Answer 1

\[f(x) = \int\limits\limits_{-\infty}^{\infty}\frac{ 1 }{ \sqrt{\pi} } \exp(-x^2 + x - b)dx =\int\limits\limits_{-\infty}^{\infty}\frac{ 1 }{ \sqrt{\pi} } \exp[-(x-0.5)^{2} -b +0.25)] dx = 1\]

Answer 2

I simplified it so that it looks like a gaussian distribution and I also know that the integral from -infinity to infinity should be 1 if it's a continuous pdf