A discrete random variable X is said to follow the Poisson distribution with parameter `m ge 0` if its p. m. f. is given by `P(X = x) = (e^(-m) m^x)/x , x = 0,1,2,....` True or False.

Answer

To determine whether the statement about the Poisson distribution is true or false, we need to analyze the provided probability mass function (p.m.f.) and compare it to the standard form of the Poisson distribution.

### Step-by-Step Solution:

1. **Understanding the Poisson Distribution**:
The probability mass function (p.m.f.) of a Poisson distribution with parameter \( m \) (where \( m \geq 0 \)) is given by:
\[ P(X = x) = \frac{e^{-m} m^x}{x!} \]
for \( x = 0, 1, 2, \ldots \)

2. **Analyzing the Given Statement**:
The statement provided is:
\[ P(X = x) = \frac{e^{-m} m^x}{x} \]
for \( x = 0, 1, 2, \ldots \)

3. **Identifying the Error**:
In the given statement, the denominator is \( x \) instead of \( x! \). The factorial \( x! \) is crucial in the definition of the Poisson distribution, as it accounts for the number of ways to arrange \( x \) events.

4. **Conclusion**:
Since the correct form of the p.m.f. includes \( x! \) in the denominator and not \( x \), the statement provided is incorrect.

Thus, the answer to the question is **False**.