The c.d.f. $$F(x)$$ associated with p.d.f. $$f(x)$$

$$f(x)=\left\{\begin{array}{cl}12 x^2(1-x), & \text { if } 0< x <1 \\ 0 ; & \text { otherwise }\end{array}\right.$$ is

The raw data $$x_1, x_2, \ldots \ldots, x_{\mathrm{n}}$$ is an A.P. with common difference $$\mathrm{d}$$ and first term $$0, \bar{x}$$ and $$\sigma^2$$ are mean and variance of $$x_{\mathrm{i}}, \mathrm{i}=1,2, \ldots \ldots \mathrm{n}$$, then $$\sigma^2$$ is

The discrete random variable $$\mathrm{X}$$ can take all possible integer values from 1 to $$\mathrm{k}$$, each with a probability $$\frac{1}{\mathrm{k}}$$, then its variance is

For 20 observations of variable $x$, if $$\sum\left(x_i-2\right)=20$$ and $$\sum\left(x_i-2\right)^2=100$$, then the standard deviation of variable $$x$$ is