Practice Book的讨论

bignipliUID: 2185755

16. A student makes 10 one-second measurements
of the disintegration of a sample of a long-lived
radioactive isotope and obtains the following
values.
3, 0, 2, 1, 2, 4, 0, 1, 2, 5
How long should the student count to establish
the rate to an uncertainty of 1 percent?
(A) 80 s
(B) 160 s
(C) 2,000 s
(D) 5,000 s
(E) 6,400 s

这道题大家都是怎么做的？看不懂呀？

fangzhao1111UID: 201099

用泊松分布

tinalovevUID: 2138528

可以说得详细点不？

guesswhatUID: 2231211

不是正态吗?我记得我们课本说poisson分布是近似的

c8s8d8UID: 2128588

同问，题目说的 10 one-second measurements测量的是什么物理量呀？而且被测样本是同一个放射性物体吗？ 那怎么会出现多个零的情况。
还有最后的问是否意思是问通过多少次采样（用时间除以10秒？可是元题目中也没有说是连续的无间隔采样）可将B类不确定度限制到正负0.01的水平（还是测量平均值的正负0.01)？
这道题感觉说得很含糊，请教高手。在线等待

cailiheng8583UID: 2188359

The mean of the ten number is <x>=2. Thus, the standard deviation of the sample is sqrt<x> approx 1.44. (Search for Poisson Distribution other problems similar to this.)

If the student wants to obtain an uncertainty of 1 percent, then

sigma/<x'>=1/100=sqrt(2 C)/(2C)=1/{sqrt(2C)},

where one assumes the average scales uniformly and C is the time to count. (Note: a good approximation of the uncertainty is given by the ratio of the standard deviation to the average, since that represents the deviation.)

Thus, one has sqrt{2 C}\=100. Thus the student should count C=5000 s.

[ 本帖最后由 cailiheng8583 于 2006-10-29 14:22 编辑 ]