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What is the difference between correlation and covariance?
Correlation is scaled to be between -1 and +1 depending on whether there is positive or negative correlation, and is dimensionless. The covariance however, ranges from zero, in the case of two independent variables, to Var(X), in the case where the two sets of data are equal. The units of COV(X,Y) are the units of X times the units of Y. correlation is the expected value of two random variables (E[XY]),whereas covariance is expected value of variations of two random variable from their expected values,
Can you compare an expected value to a calculated value?
Yes, an expected value represents the theoretical average outcome of a random variable based on its probability distribution, while a calculated value is the result obtained from actual observations or experiments. Comparing the two can help assess the accuracy of predictions and the reliability of the model used to derive the expected value. Discrepancies between the expected and calculated values can indicate potential biases, errors in the model, or the influence of random variation in the data.
How many types of randam variables in Statistics?
In statistics, there are two main types of random variables: discrete random variables and continuous random variables. Discrete random variables take on a countable number of distinct values, such as the outcome of rolling a die. In contrast, continuous random variables can take on an infinite number of values within a given range, such as the height of individuals. Each type has its own probability distribution and methods of analysis.
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.
If you break a stick 12 inches long in two at a random point what is the expected length of the smaller piece?
the length would be anywhere between 1 and 1/2 and so the expected value is 1/4
Why not simply use the mean value of the regressand as its best value?
Variance" is a mesaure of the dispersion of the probability distribution of a random variable. Consider two random variables with the same mean (same aver-age value). If one of them has a distribution with greater variance, then, roughly speaking, the probability that the variable will take on a value far from the mean is greater.
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).
How do you compute the probability distribution of a function of two Poisson random variables?
we compute it by using their differences
Difference between mean and expected value?
For a population the mean and the expected value are just two names for the same thing. For a sample the mean is the same as the average and no expected value exists.
When are two random samples dependent?
Two random samples are dependent if each data value in one sample can be paired with a corresponding data value in the other sample.
What does it mean for economic variables to positively related?
if two variables are positively related,it means that the two variables change in the same direction.that is,if the value of one of the variables increases,the value of the other variable too will increase.for example,if employment as an economic variable increases in a country,and price of goods too increases then we can say that these two variables(employment and price) are positively related
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.
