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Will the sum of two normally distributed random variables be normally distributed if the random variables are independent?
Wiki User
∙ 15y ago
Yes, and the new distribution has a mean equal to the sum of the means of the two distribution and a variance equal to the sum of the variances of the two distributions. The proof of this is found in Probability and Statistics by DeGroot, Third Edition, page 275.
Wiki User
∙ 15y ago
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What is the The sum of two normally distributed random variables?
The sum of two random variables that are normally distributed will be also be normally distributed. Use the link and check out the article. It'll save a cut and paste.
ARE All continuous random variables are normally distributed?
YES.
What does the Central Limit Theorem state?
The Central Limit Theorem (abbreviated as CLT) states that random variables that are independent of each other will have a normally distributed mean.
How chi square distribution is extension of normal distribution?
Given "n" random variables, normally distributed, and the squared values of these RV are summed, the resultant random variable is chi-squared distributed, with degrees of freedom, k = n-1. As k goes to infinity, the resulant RV becomes normally distributed. See link.
Briefly explain in your own words The Central Limit Theorem?
According to the Central Limit Theorem, the arithmetic mean of a sufficiently large number of iterates of independent random variables at a given condition is normally distributed. This is based on the condition that each random variable has well defined-variance and expected value.
What is the The sum of two normally distributed random variables?
The sum of two random variables that are normally distributed will be also be normally distributed. Use the link and check out the article. It'll save a cut and paste.
ARE All continuous random variables are normally distributed?
YES.
What does the Central Limit Theorem state?
The Central Limit Theorem (abbreviated as CLT) states that random variables that are independent of each other will have a normally distributed mean.
Will the variance of the difference of two independent normally distributed random variables be equal to the SUM of the variances of the two distributions?
Yes it is. That is actually true for all random vars, assuming the covariance of the two random vars is zero (they are uncorrelated).
What do you want your residuals to be in statistics?
For the purpose of analyses, they should be independent, identically distributed random variables. But the ideal is that they are all 0.
How chi square distribution is extension of normal distribution?
Given "n" random variables, normally distributed, and the squared values of these RV are summed, the resultant random variable is chi-squared distributed, with degrees of freedom, k = n-1. As k goes to infinity, the resulant RV becomes normally distributed. See link.
How did the normal distribution get its name?
According to the Central Limit Theorem the sum of [a sufficiently large number of] independent, identically distributed random variables has a Gaussian distribution. This is true irrespective of the underlying distribution of each individual random variable.As a result, many of the measurable variables that we come across have a Gaussian distribution and consequently, it is also called the normal distribution.According to the Central Limit Theorem the sum of [a sufficiently large number of] independent, identically distributed random variables has a Gaussian distribution. This is true irrespective of the underlying distribution of each individual random variable.As a result, many of the measurable variables that we come across have a Gaussian distribution and consequently, it is also called the normal distribution.According to the Central Limit Theorem the sum of [a sufficiently large number of] independent, identically distributed random variables has a Gaussian distribution. This is true irrespective of the underlying distribution of each individual random variable.As a result, many of the measurable variables that we come across have a Gaussian distribution and consequently, it is also called the normal distribution.According to the Central Limit Theorem the sum of [a sufficiently large number of] independent, identically distributed random variables has a Gaussian distribution. This is true irrespective of the underlying distribution of each individual random variable.As a result, many of the measurable variables that we come across have a Gaussian distribution and consequently, it is also called the normal distribution.
Is Statistically independent random variables are uncorrelated and vice versa?
the statistically independent random variables are uncorrelated but the converse is not true ,i want a counter example,
Briefly explain in your own words The Central Limit Theorem?
According to the Central Limit Theorem, the arithmetic mean of a sufficiently large number of iterates of independent random variables at a given condition is normally distributed. This is based on the condition that each random variable has well defined-variance and expected value.
What is the role of the stochastic error term in regression analysis?
Regression analysis is based on the assumption that the dependent variable is distributed according some function of the independent variables together with independent identically distributed random errors. If the error terms were not stochastic then some of the properties of the regression analysis are not valid.
What is importance of central limit theorem?
The importance is that the sum of a large number of independent random variables is always approximately normally distributed as long as each random variable has the same distribution and that distribution has a finite mean and variance. The point is that it DOES NOT matter what the particular distribution is. So whatever distribution you start with, you always end up with normal.
How do you see that the sampling distribution of the mean is normal?
According to the Central Limit Theorem, the mean of a sufficiently large number of independent random variables which have a well defined mean and a well defined variance, is approximately normally distributed.The necessary requirements are shown in bold.According to the Central Limit Theorem, the mean of a sufficiently large number of independent random variables which have a well defined mean and a well defined variance, is approximately normally distributed.The necessary requirements are shown in bold.According to the Central Limit Theorem, the mean of a sufficiently large number of independent random variables which have a well defined mean and a well defined variance, is approximately normally distributed.The necessary requirements are shown in bold.According to the Central Limit Theorem, the mean of a sufficiently large number of independent random variables which have a well defined mean and a well defined variance, is approximately normally distributed.The necessary requirements are shown in bold.
