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Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function, $f(x),$ as shown in the figure.

Consider a $1$ bit quantizer that maps positive samples to value $\alpha$ and others to value $\beta.$ If $\alpha^{\ast}$ and $\beta^{\ast}$ are the respective choices for $\alpha$ and $\beta$ that minimize the mean square quantization error, then $(\alpha^{\ast} – \beta^{\ast}) = $____________ (rounded off to two decimal places).

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