- #1
Josh S Thompson
- 111
- 4
Why do people say that RVs that have the normal distribution has a constant variance. What does that mean constant variance.
A normal distribution is a type of probability distribution that is symmetric around the mean and follows a bell-shaped curve. It is often used to model natural phenomena and can be described by its mean and standard deviation.
The central limit theorem states that when independent random variables are added, their sum tends toward a normal distribution, regardless of the original distribution of the variables. This makes the normal distribution useful in statistical analysis, as many real-world phenomena can be approximated by the sum of many random variables.
The variance of a normal distribution is equal to the square of its standard deviation. It can also be calculated by taking the sum of the squared differences between each data point and the mean, divided by the total number of data points.
Constant variance is important in a normal distribution because it ensures that the shape of the distribution remains consistent. If the variance is not constant, the distribution may become skewed and the mean and standard deviation may not accurately represent the data.
The normal distribution is often used in hypothesis testing to determine the probability of obtaining a certain result by chance. It allows researchers to compare their sample data to a known normal distribution and calculate the likelihood of their results occurring by random chance. This can help determine the significance of their findings.