# 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

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Self-study questions (including textbook exercises, old exam papers, and homework) that seek to understand the concepts are welcome, but those that demand a solution need to indicate clearly at what step help or advice are needed. For help writing a good self-study question, please visit the meta pages." – Tim
If this question can be reworded to fit the rules in the help center, please edit the question.

• 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 $$f(0)=\frac{1}{\sqrt{2\pi}2}$$.