State whether True or False:
If n is very large and p is very small then X follows Poisson distribution with n = m p.

Answer

To determine whether the statement is true or false, we need to analyze the conditions given in the question regarding the Poisson distribution.

### Step-by-Step Solution:

1. **Understanding the Poisson Distribution**:
The Poisson distribution is often used to model the number of events occurring in a fixed interval of time or space when these events happen with a known constant mean rate and independently of the time since the last event.

2. **Parameters of the Poisson Distribution**:
The Poisson distribution is characterized by a single parameter, λ (lambda), which is the average number of occurrences in the interval.

3. **Conditions Given**:
The question states that n is very large and p is very small. In the context of a binomial distribution, if we have n trials and the probability of success in each trial is p, then the mean of the binomial distribution is given by np.

4. **Using the Poisson Approximation**:
The Poisson distribution can be used as an approximation to the binomial distribution when n is large and p is small, under the condition that the product np (which is λ) remains constant. This means that as n increases, p must decrease in such a way that np approaches a constant value.

5. **Analyzing the Statement**:
The statement claims that if n is very large and p is very small, then X follows a Poisson distribution with n = mp. However, this is incorrect because for the Poisson approximation to hold, we need np = m (a constant), not n = mp.

6. **Conclusion**:
Since the condition n = mp contradicts the requirement for the Poisson approximation (which requires np to be constant), we conclude that the statement is **False**.

### Final Answer:
**False**