Can any one help me to calculate this function : $$f(y)=\max\limits_{\mu>0}[\exp(\frac{-n\mu^{2}}{\sigma^{2}})\exp(\frac{2\mu}{\sigma^{2}}\sum_{k=1}^{n}y_{k})]$$ where $y_{k}$ is random variable with normal distribution. $$$$ Thank you in advance.
Sorry, I had forgotten to put the second power of $\mu$ in first exponential(I modified it).