Let a {\displaystyle a} and b {\displaystyle b} be real numbers and let f ( x ) = { x = 0 if x < a e b x if x ≥ a . {\displaystyle f(x)={\begin{cases}x=0&{\text{if}}\ x<a\\e^{bx}&{\text{if}}\ x\geq a.\end{cases}}} Find (with justification) the values for a {\displaystyle a} and b {\displaystyle b} such that f ( x ) {\displaystyle f(x)} is a probability density function with expected value equal to 0 {\displaystyle 0} .
