# 1. Introduction

This R program demonstrates how to fit a Poisson distribution to a given set of data. The Poisson distribution is a probability distribution that describes the number of events occurring in a fixed interval of time or space if these events happen with a known constant mean rate and independently of the time since the last event.

# 2. Program Steps

1. Generate or provide a dataset that likely follows a Poisson distribution.

2. Fit the Poisson distribution to the data by estimating the rate parameter (lambda).

3. Print the estimated rate parameter.

# 3. Code Program

``````# Step 1: Generate a dataset
# For illustration, generating data using rpois, ideally this data should be from real observations
data <- rpois(100, lambda = 4)  # 100 data points with lambda = 4

# Step 2: Fit the Poisson distribution to the data
# Estimate the rate parameter (lambda) as the mean of the data
lambda_estimate <- mean(data)

# Step 3: Print the estimated rate parameter
print("Estimated lambda (rate parameter) for Poisson distribution:")
print(lambda_estimate)

``````

### Output:

```Estimated lambda (rate parameter) for Poisson distribution:
[Estimated Lambda Value]
```

### Explanation:

1. rpois(100, lambda = 4): Generates 100 data points following a Poisson distribution with a lambda (rate parameter) of 4. In practice, this data would be observed rather than generated.

2. mean(data): Calculates the mean of the dataset, which is the estimator for the lambda parameter in the Poisson distribution.

3. print("Estimated lambda (rate parameter) for Poisson distribution:"), print(lambda_estimate): Prints the estimated lambda value.