10.
Conclusion: The risk of lung cancer for smoker is 5 times as much as that for ordinary people.
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2.3 Binomial Distribution P ( white ball)=0.8 P ( yellow ball )=0.2
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In general, if : the probability of an event appearing in a trial n : times of independently repeated trials X : random variable, total times of appearing such an event, then the probability of X = x This variable X is called a binomial variable , or say X following a binomial distribution , denoted as Why is it called Binomial? See following expansion:
Example Pulse count of radio active isotope( 同位素 ).
Large n and 0-1 : Divide the period into n sub-intervals, possible numbers of pulses in a sub-interval = 0 or 1
Rare event :
Independent
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It can be proved, When n ->∞, the will tend to In general, if the probability function of a random variable X has the above shape , then we say that this variable follows a Poisson distribution with parameter , denoted by .
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Example ： Red cell count on glass slide. Since Divide the glass slide into n small grids ---- big n , 0 or 1 ； P (a red cell) = ---- small probability ; With or without a cell ---- independent ; Therefore, Number of cells ~ Poisson distribution
In practice, The shape of frequency histograms of many
continuous random variables looks like this:
taller around center, shorter on two sides and symmetric.
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μ 1 μ 2 μ 3 Two parameters: population mean population variance Normal distribution denoted by
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Standard normal distribution , , To any normal variable , after a transformation of standardization Z is called with standardized normal deviate or Z-value , or Z-score
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2.5.2 Area under the normal probability density curve
A table for standard normal distribution is usually
attached in most textbooks of statistics. (P. 479)
2. If the variable does not follow a normal distribution, then find out the percentile and percentile
Therefore, reference range:
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Example Based on the hemoglobin data of 120 healthy females ， , ; and the histogram shows it approximately follows a normal distribution. Please estimate the two-sided 95% reference range for females.
40.
Example The infectious rate of hookworm( 钩虫 ) is 13% ， if randomly select 150 people ， what is the probability that at least 20 of them being infected ？ The probability that at least 20 of them being infected is 50% 。 Area of the rectangles on
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