12. 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:
17. 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 .
18. 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
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20. 2.4.2 Plot of probability function , positive skew; , approximately symmetric
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25. μ 1 μ 2 μ 3 Two parameters: population mean population variance Normal distribution denoted by
26. 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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31. Critical value : Two sided critical value : One sided critical value
32. Distribution of X 1 + X 2 still follow a normal distribution When X 1 and X 2 are independent,
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35. 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.
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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