The standard deviation of a poisson distribution is 4 then its mean is

Options

A. 4
B. 16
C. 2
D. 8

Answer

To find the mean of a Poisson distribution given that its standard deviation is 4, we can follow these steps:

### Step-by-step Solution:

1. **Understand the relationship between mean and variance in a Poisson distribution**:
- In a Poisson distribution, the mean (μ) is equal to the variance (σ²). This means that if we denote the mean by λ, we have:
\[ \mu = \lambda \quad \text{and} \quad \sigma^2 = \lambda \]

2. **Relate standard deviation to variance**:
- The standard deviation (σ) is the square root of the variance. Therefore, we can express this as:
\[ \sigma = \sqrt{\sigma^2} = \sqrt{\lambda} \]

3. **Set up the equation using the given standard deviation**:
- According to the problem, the standard deviation is given as 4. Thus, we can write:
\[ \sqrt{\lambda} = 4 \]

4. **Square both sides to solve for λ**:
- To eliminate the square root, we square both sides of the equation:
\[ \lambda = 4^2 \]
- This simplifies to:
\[ \lambda = 16 \]

5. **Conclusion**:
- Since the mean (μ) of the Poisson distribution is equal to λ, we conclude that:
\[ \text{Mean} = 16 \]

### Final Answer:
The mean of the Poisson distribution is **16**.

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