A random variable x takes the values 0, 1, 2, 3 and its mean is 1.3. If P(x=3)=2 P(x=1) and P(x = 2) = 0.3, then P(x = 0) =

Range={0,1,2,3}

$\mathrm{Let} \mathrm{P}\left(\mathrm{X}=0\right)=\mathrm{a},\mathrm{P}\left(\mathrm{X}=1\right)=\mathrm{b},\Rightarrow \mathrm{P}\left(\mathrm{X}=3\right)=2\mathrm{b},\mathrm{P}\left(\mathrm{X}=2\right)=0.3$

$\sum _{ }^{ }P\left(X=x_i\right)=1\Rightarrow a+b+0.3+2b=1\Rightarrow \boxed{a+3b=0.7}$

$\mathrm{\mu }=\sum {\mathrm{x}}_{\mathrm{r}}.\mathrm{P}\left(\mathrm{x}={\mathrm{x}}_{\mathrm{r}}\right)=0\left(\mathrm{a}\right)+1\left(\mathrm{b}\right)+2\left(0.3\right)+3\left(2\mathrm{b}\right)=1.3$

$7b=0.7\Rightarrow b=0.1$

$a+3\left(0.1\right)=0.7\Rightarrow a=0.4$

$P\left(X=0\right)=0.4$