**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