Mean of a Uniform Distribution

The mean of a uniform distribution on the interval (-3, 7) can be calculated using the following formula:

Mean (μ) = (a + b) / 2

Where:
- a is the lower limit of the interval (-3 in this case)
- b is the upper limit of the interval (7 in this case)

Calculating the Mean

Using the formula, we can calculate the mean of the uniform distribution as follows:

Mean (μ) = (-3 + 7) / 2

Mean (μ) = 4 / 2

Mean (μ) = 2

Hence, the mean of the uniform distribution on the interval (-3, 7) is 2.

Explanation

The mean of a distribution represents the average value of the random variable. In this case, the random variable X has a uniform distribution on the interval (-3, 7), which means that all values within this interval are equally likely to occur.

The formula for calculating the mean of a uniform distribution takes the average of the lower and upper limits of the interval. In this case, the lower limit is -3 and the upper limit is 7.

By substituting these values into the formula, we find that the mean of the uniform distribution is 2. This means that, on average, the random variable X will take a value of 2.

The mean is a measure of central tendency and provides insight into the "typical" value of the random variable. However, it is important to note that the mean does not necessarily represent a value that the random variable will take on. In this case, the random variable can take on any value within the interval (-3, 7), but on average, it will be closer to 2.