Bernoulli distribution is a particular case of binomial distribution if n = ...........

Options

A. 4
B. 10
C. 2
D. 1

Answer

To solve the question regarding the Bernoulli distribution being a particular case of the binomial distribution, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- The **Bernoulli distribution** describes a random experiment that has exactly two possible outcomes: success (with probability \( p \)) and failure (with probability \( 1 - p \)).
- The **binomial distribution** generalizes the Bernoulli distribution to \( n \) independent Bernoulli trials.

2. **Identifying the Parameters**:
- The binomial distribution is defined by two parameters: \( n \) (the number of trials) and \( p \) (the probability of success in each trial).

3. **Special Case of Binomial Distribution**:
- The Bernoulli distribution can be seen as a binomial distribution with only one trial. This means that if we set \( n = 1 \), we are conducting a single Bernoulli trial.

4. **Conclusion**:
- Therefore, the Bernoulli distribution is a particular case of the binomial distribution when \( n = 1 \).

### Final Answer:
The Bernoulli distribution is a particular case of the binomial distribution if \( n = 1 \).

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