# 1. Introduction

This R program calculates the mean, variance, and standard deviation for a given continuous probability distribution. Unlike discrete distributions, continuous distributions require integration to find these statistics.

For demonstration purposes, let's consider a normal distribution, which is a common type of continuous probability distribution.

# 2. Program Steps

1. Define the parameters of the normal distribution (mean and standard deviation).

2. Use R's built-in functions to calculate the mean, variance, and standard deviation.

3. Print the results.

# 3. Code Program

``````# Step 1: Define the parameters of the normal distribution
mean_value <- 50
sd_value <- 10

# Step 2: Use R's built-in functions
# For a normal distribution, the mean is the mean value, variance is square of standard deviation, and the standard deviation is the sd value.
variance_value <- sd_value^2

# Step 3: Print the results
print("Mean of the distribution:")
print(mean_value)
print("Variance of the distribution:")
print(variance_value)
print("Standard deviation of the distribution:")
print(sd_value)

``````

### Output:

```Mean of the distribution:
[50]
Variance of the distribution:
[100]
Standard deviation of the distribution:
[10]
```

### Explanation:

1. mean_value <- 50 and sd_value <- 10: Sets the mean and standard deviation for the normal distribution.

2. The mean of the normal distribution is its mean parameter.

3. The variance of the normal distribution is the square of its standard deviation (sd_value^2).

4. print("Mean of the distribution:"), print(mean_value): Prints the mean of the distribution.

5. print("Variance of the distribution:"), print(variance_value): Prints the variance of the distribution.

6. print("Standard deviation of the distribution:"), print(sd_value): Prints the standard deviation of the distribution.

Note: This approach uses a specific normal distribution. For other continuous distributions, calculations may vary and might involve integrals or other functions specific to that distribution.