白努力試驗 - 成功與失敗
常常會遇到只有兩種實驗結果的試驗, 成功(Successes)以及 失敗(Failures).
通常只要涉及只有兩種不同的結果實驗即可適用 Bernoulli Trial. 舉例如下:
- Inspect a specified number of items coming off a production line and
count the number of defectives.
- Survey a sample of voters and observe how many favor a reduction of
public spending on welfare.
- Analyze the blood specimens of a number of rodents and count how many
carry a particular viral infection.
- Examine the case histories of a number of births and count how many
involved delivery by Caesarean section.
- Each trial yields one of two outcomes, technically called success (S)and failure (F).
- For each trial, the probability of success P(S) is the same and is
deonted by p=P(S). The probability of failure is then P(F)=1-p for each
trial and is denoted by q, so that p+q=1.
- Trials are independent. The probability of success in a trial does not
change given any information about the outcomes of other trials.
白努力試驗, 最簡單的例子即是投擲一個公平的銅板, 發生正面代表 (S),
發生反面代表 (F), 所以我們可得 p=q=1/2