Is variance affected by skewness?
The variance measures the squared differences of the data from the mean and skewness measures the cubed differences of the data from the mean. While a variance can never be a negative number, the measure of skewness can and this is how we determine if the data are skewed right of left.
What is the difference between T-distribution and normal distribution?
The normal distribution assumes that the population standard deviation is known. The t-distribution is defined by the degrees of freedom. These are related to the sample size. The t-distribution is most useful for small sample sizes, when the population standard deviation is not known, or both.
Can a continuous distribution have the same mean and variance?
Another example is multimodality: A continuous distribution with multiple modes can have the same mean and variance as a distribution with a single mode, while clearly they are not identically distributed. For example, consider a mixture of two normal distributions, each with σ 2 = 1, but their means are 2 and − 2, respectively.
What happens if two random variables have the same mean?
For example, consider a mixture of two normal distributions, each with σ 2 = 1, but their means are 2 and − 2, respectively. The resulting mixture will have a mean of μ = 0 and a variance of σ 2 = 5, which is the same expectation and variance as a single normal distribution N ( 0, 5):
How to compare the variance of two variables?
To compare the variances of two quantitative variables, the hypotheses of interest are: The last two alternatives are determined by how you arrange your ratio of the two sample statistics. We will rely on Minitab to conduct this test for us. Minitab offers three (3) different methods to test equal variances.
Is it possible to determine the shape of a probability distribution?
In short: No. There are several properties of a probability distribution that need not affect its mean and variance, but do determine its shape. For example, a Poisson distribution with λ = 1 has expected value λ = 1 and variance λ = 1.