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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.
Will the sum of two normally distributed random variables be normally distributed if the random variables are independent?
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.
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.
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.
Continuous random variables are obtained from data that can be measured rather than counted?
true
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.
Will the sum of two normally distributed random variables be normally distributed if the random variables are independent?
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.
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.
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).
Continuous random variables are obtained from data that can be measured rather than counted?
true
What is the importance of distribution functions to stochastic processes?
Stochastic processes are families of random variables. Real-valued (i.e., continuous) random variables are often defined by their (cumulative) distribution function.
Are all variables that are approximentaly normally distributed be transformed to standard normal variables?
Yes, to approximately standard normal.If the random variable X is approximately normal with mean m and standard deviation s, then(X - m)/sis approximately standard normal.
Are negative numbers discrete random variables?
Discrete variables must be countable and not negative. So no a negative number must be a continuous variable.
When you draw a sample from a normal distribution what can you conclude about the sample distribution?
The answer depends on how the sample is selected. If it is a simple random sample, of size n, then it is distributed approximately normally with the same mean as the population mean.The answer depends on how the sample is selected. If it is a simple random sample, of size n, then it is distributed approximately normally with the same mean as the population mean.The answer depends on how the sample is selected. If it is a simple random sample, of size n, then it is distributed approximately normally with the same mean as the population mean.The answer depends on how the sample is selected. If it is a simple random sample, of size n, then it is distributed approximately normally with the same mean as the population mean.
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.
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.
