Question

four macrostates of a system have 2,6,16 and 2 microstates respectively a physical quantity was measured be 1,3,4 and 7 in those state respectively find<x>
Answer 49/13

Answer 1

$$\left< x\right>=\frac{\sum x n_x}{\sum n_x}$$

$$\sum x n_x =(2)(1)+(6)(3)+(16)(4)+(2)(7)=98$$

$$\sum n_x =(2)+(6)+(16)+(2)=26$$

$$\left< x\right>=\frac{98}{26}=\frac{49}{13}$$