Can two different distributions have same mean and variance?

Can two different distributions have same mean and variance?

As @Glen_b pointed out, skew and kurtosis are not the only things to take into consideration. 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.

What is the variance of the mean of the two values?

The variance (σ2) is a measure of how far each value in the data set is from the mean. Here is how it is defined: Subtract the mean from each value in the data. This gives you a measure of the distance of each value from the mean.

What is the variance of the difference of two random variables?

For independent random variables X and Y, the variance of their sum or difference is the sum of their variances: Variances are added for both the sum and difference of two independent random variables because the variation in each variable contributes to the variation in each case.

What does it mean if two distributions have the same mean?

Nevertheless, comparing means and standard deviations do not guarantee that the distributions are similar — you may have two distributions with the same mean and standard deviation that, e.g., have different skewness and/or kurtosis. So, to compare distributions, you can use the two-sample Kolmogorov–Smirnov test.

What is the variance of the difference between two means?

When the population variances are known, the difference of the means has a normal distribution. The variance of the difference is the sum of the variances divided by the sample sizes.

How do you know if two distributions have the same mean?

Z-test
The simplest way to compare two distributions is via the Z-test. The error in the mean is calculated by dividing the dispersion by the square root of the number of data points. In the above diagram, there is some population mean that is the true intrinsic mean value for that population.

What is the formula for calculating normal distribution?

Normal Distribution is calculated using the formula given below. Z = (X – µ) /∞. Normal Distribution (Z) = (145.9 – 120) / 17. Normal Distribution (Z) = 25.9 / 17.

What is a normal distribution plot?

A normal distribution in statistics is distribution that is shaped like a bell curve. With a normal distribution plot, the plot will be centered on the mean value. In a normal distribution, 68% of the data set will lie within ±1 standard deviation of the mean.

What is a standard complex Gaussian random variable?

The standard complex normal random variable or standard complex Gaussian random variable is a complex random variable whose real and imaginary parts are independent normally distributed random variables with mean zero and variance /.

How do you calculate standard distribution?

Standard Normal Distribution is calculated using the formula given below. Z = (X – μ) / σ. Standard Normal Distribution (Z) = (75.8 – 60.2) / 15.95. Standard Normal Distribution (Z) = 15.6 / 15.95.