Science:Math Exam Resources/Courses/MATH101 C/April 2025/Question 09/Statement

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