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). 而可以用一個參數(parameter)來代表未知的母體. 並非一定要成功及失敗的結果實驗才適用, 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:

(a)

Inspect a specified number of items coming off a production line and count the number of defectives.

(b)

Survey a sample of voters and observe how many favor a reduction of public spending on welfare.

(c)

Analyze the blood specimens of a number of rodents and count how many carry a particular viral infection.

(d)

Examine the case histories of a number of births and count how many involved delivery by Caesarean section.

Bernoulli Trials

1

Each trial yields one of two outcomes, technically called success (S)and failure (F).

2

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.

3

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