已知随机变量 $\xi$ 的取值为 $i(i=0,1,2)$. 若 $P(\xi=0)=\frac{1}{5}, \quad E(\xi)=1$, 则 $D(2 \xi-3)=(\quad)$
由题意, 设 $P(\xi=1)=p$, 则 $P(\xi=2)=1-rac{1}{5}-p=rac{4}{5}-p$,又 $E(\xi)=0 	imes rac{1}{5}+1 	imes p+2\left(rac{4}{5}-p
ight)=1$, 解得 $p=rac{3}{5}$,所以 $P(\xi=1)=rac{3}{5}, P(\xi=2)=rac{1}{5}$,则 $D(\xi)=rac{1}{5}(1-0)^{2}+rac{3}{5}(1-1)^{2}+rac{1}{5}(1-2)^{2}=rac{2}{5}$,所以 $D(2 \xi-3)=4 D(\xi)=rac{8}{5}$.故答案为: C.