Understanding Uniform Distribution
In a uniform distribution, every value within a specified range is equally likely to occur. For a random variable x that follows a uniform distribution on the interval [-3, 7], we can determine its mean by using the formula for the mean of a uniform distribution.
Mean of Uniform Distribution
The mean (μ) of a uniform distribution defined on the interval [a, b] is calculated using the formula:
- μ = (a + b) / 2
In this case:
- a = -3
- b = 7
Calculating the Mean
Now, substituting the values into the formula:
- μ = (-3 + 7) / 2
This simplifies to:
- μ = 4 / 2
- μ = 2
Thus, the mean of the distribution is 2.
Key Points to Remember
- The mean represents the center of the distribution.
- A uniform distribution implies all values in the range are equally probable.
- The mean value provides a useful summary of the distribution's central tendency.
Conclusion
The mean of the uniform distribution for the random variable x over the interval [-3, 7] is 2. This value indicates where the center of the distribution lies, reflecting the average outcome of random samples drawn from this interval.