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A random variable $X$ takes values $-1$ and $+1$ with probabilities $0.2$ and $0.8$, respectively. It is transmitted across a channel which adds noise $N,$ so that the random variable at the channel output is $Y=X+N$. The noise $N$ is independent of $X,$ and is uniformly distributed over the interval $[-2,2].$ The receiver makes a decision

$$\hat{X}= \left\{\begin{matrix}
 -1,& \text{if} \quad Y \leq \theta  \\
 +1,& \text{if} \quad Y > \theta
\end{matrix}\right. $$
where the threshold $\theta \in [-1,1]$ is chosen so as to minimize the probability of error $Pr[ \hat{X} \neq X].$ The minimum probability of error, rounded off to $1$ decimal place, is _________.
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