Here the Variance Var(x) formula is given
Here as you can see Var(x) formula
$$Var(X)= \frac{4-\pi}{2}\sigma ^2$$
Now the fact is known that
1)Variance general formula is square of standard deviation = σˆ2
2)and standard deviation = σ
but on LHS of the formula Var(x) is given which is Variance and that is equal to σˆ2 and on RHS also in the formula σˆ2 is included
how to differentiate between the two - the var(x) on left side and sigma on right side ,is there any distinction here ? and what does σˆ2 on RHS mean ?
same goes for other formulae in the pic included - what does σ mean there and is it same as general standard deviation ?
we also see in gaussian normal distribution ( bells graph ) - var(x) is σ and expectation E(x) or mean is μ but not in rayleigh , although the notation is used in the rayleigh mean and var(x) formula
$\sigma^2$ here is not "variance " but only a parameter of the distribution. To calculate the variance and verify the result in your link use the definition
$$\mathbb{V}[X]= \mathbb{E}[X^2]-\mathbb{E}^2[X]$$