Expressing as a probability density function [closed]

The measuring error x is a normal random variable. Variance of the error = 4. If distribution of x can be shown by a probability density function f(x), how would you find the analytical expression of f(x)?

closed as off-topic by Tim♦Apr 11 at 20:46

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• Do I miss something or is this question ill-posed? You say "x is a normal random variable", so it's distribution is normal. Given the variance=4, so $\sigma = 2$, that's a $\mathcal{N}(\mu,2)$ distribution with unknown $\mu$. Which has a maximum of $\frac{1}{\sqrt{2\pi}\sigma}\approx 0.199471$ at $\mu$. – corey979 Apr 11 at 19:39

Probably the error is assumed to be zero mean. Thus it has a N(0,4) distribution with density $$f(x)=\frac{1}{\sqrt{2\pi}2}e^{-x^2/8}$$. The mode is at the mean of 0, with $$f(0)=\frac{1}{\sqrt{2\pi}2}$$.