455. Based on a sample of size $n=41$, a biased estimate $D_{\text {v }}=3$ of the population variance was found. Find the unbiased estimate of the population variance.
Solution. The desired mixed estimate is equal to the corrected variance:

$$
s^{2}=\frac{n}{n-1} D_{B}=\frac{41}{40} \cdot 3=3.075
$$