已知随机变量 X 的分布列如下表:

![](https://cdn.mathpix.com/cropped/2024_04_19_ff3e626f3bf93f0a342dg-
由题意 $\left\{egin{array}{l}rac{1}{2}+b+rac{1}{4}=1 \ E(X)=0 	imes rac{1}{2}+2 b+rac{1}{4} a=2, 	ext { 解得 } b=rac{1}{4}, a=6 	ext {; }\end{array}
ight.$所以 $D(X)=(0-2)^{2} 	imes rac{1}{2}+(2-2)^{2} 	imes rac{1}{4}+(6-2)^{2} 	imes rac{1}{4}=6$,所以 $D(2 X-1)=2^{2} \cdot D(X)=24$. 故答案为: $rac{1}{4}, 24$.