Conclusion: The risk of lung cancer for smoker is 5 times as much as that for ordinary people.
2.3 Binomial Distribution P ( white ball)=0.8 P ( yellow ball )=0.2
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 :
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 .
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
2. If the variable does not follow a normal distribution, then find out the percentile and percentile
Therefore, reference range:
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.
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