What does it mean when mean and variance are equal?

What does it mean when mean and variance are equal?

Equal variances (homoscedasticity) is when the variances are approximately the same across the samples. If you are comparing two or more sample means, as in the 2-Sample t-test and ANOVA, a significantly different variance could overshadow the differences between means and lead to incorrect conclusions.

What distribution has same mean and variance?

Poisson distribution
The Poisson distribution has a particularly simple mean, E ( X ) = λ , and variance, V ( X ) = λ .

Do identically distributed variables have the same mean?

Notice that because the variables are identically distributed all the means (and variances) have to be the same, so we are just adding µ together n times (and similarly for σ2.

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):

Is that mean they have same mean and variance?

Is that mean they have same mean and variance? It is more general than this. It means that F X ( t) = P ( X ≤ t) = P ( Y ≤ t) = F Y ( t), for all t. Then, in particular, if the mean and variance exist, then their values coincide for these variables.

What does the mean of the same distribution mean?

It means that F X ( t) = P ( X ≤ t) = P ( Y ≤ t) = F Y ( t), for all t. Then, in particular, if the mean and variance exist, then their values coincide for these variables. The functions F X ( t) = P ( X ≤ t) and F Y ( t) = P ( Y ≤ t) are termed the distribution functions of the variables X and Y, respectively. See

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.