一个统计学的问题Computers are ofter used to randomly generate digits
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一个统计学的问题
Computers are ofter used to randomly generate digits of telephone numbers to be called for surveys.Each digit has the same chance of being selected.Construct a table representing the probability distribution for the digits selected,find its mean,find its standard deviation,and describe the shape of the shape of the probability histogram.
Computers are ofter used to randomly generate digits of telephone numbers to be called for surveys.Each digit has the same chance of being selected.Construct a table representing the probability distribution for the digits selected,find its mean,find its standard deviation,and describe the shape of the shape of the probability histogram.
Suppose there are N digits selected:d1,d2,...,dN.
Due to each digit has the same chance to be selected,the probability distribution of the digits selected is a kind of uniform distribution.
So,the mean = (d1 + d2 + ...+ dN)/N.
The mean of square = [(d1)^2 + (d2)^2 + ...+ (dN)^2]/N.
The deviation = the mean of square - the square of mean
= [(d1)^2 + (d2)^2 + ...+ (dN)^2]/N - [(d1 + d2 + ...+ dN)/N]^2
The stardard deviation = the square root of the deviation
= [the deviation]^(1/2)
In the probability histogram,all the digits have the same probability(=1/N),means that all the probability of digits have the the same height(= 1/N).
Due to each digit has the same chance to be selected,the probability distribution of the digits selected is a kind of uniform distribution.
So,the mean = (d1 + d2 + ...+ dN)/N.
The mean of square = [(d1)^2 + (d2)^2 + ...+ (dN)^2]/N.
The deviation = the mean of square - the square of mean
= [(d1)^2 + (d2)^2 + ...+ (dN)^2]/N - [(d1 + d2 + ...+ dN)/N]^2
The stardard deviation = the square root of the deviation
= [the deviation]^(1/2)
In the probability histogram,all the digits have the same probability(=1/N),means that all the probability of digits have the the same height(= 1/N).
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