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jimmy1
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Suppose I had n random variables, all of which have the same distribution but different mean and variances. How can I formally describe the distribution of these n random variables.
Yes.jimmy1 said:Would this distribution be known as a joint distribution?
Maybe. Maybe not.Would I be able to use the multivariate normal distribution??
Let me rephrase your problem in terms of discrete distributions -- maybe it will help you understand what the problem is.jimmy1 said:Thanks for help, Hurkyl.
So, is there any general formula or method for getting the joint distribution of n random variables. For example, if all the random variables were exponential
0.05 0.20 0.10 | 0.35
0.15 0.05 0.05 | 0.25
0.10 0.15 0.15 | 0.40
-----------------+-----
0.30 0.40 0.30 | 1.00
* * * | 0.35
* * * | 0.25
* * * | 0.40
-----------------+-----
0.30 0.40 0.30 | 1.00
What do you mean by "dependency?" If you weren't asking the question you're asking, I would have assumed that parenthetical meant you already knew the joint distribution.(and I knew all the dependencies of the n random variables), is there a method??
There only seems to be multivariate normal and binomial distributions??
Describing the distribution of n random variables refers to the process of quantifying and understanding the patterns and characteristics of a set of random variables. This typically involves calculating measures such as mean, median, and standard deviation, as well as visualizing the data through graphs or charts.
Describing the distribution of n random variables allows us to gain insights into the underlying patterns and relationships within the data. This information can be used to make predictions, identify outliers, and make informed decisions based on the data.
Some common methods for describing the distribution of n random variables include calculating measures of central tendency (such as mean, median, and mode), measures of variability (such as range, variance, and standard deviation), and creating visual representations (such as histograms, box plots, and scatter plots).
A distribution is considered normal if it follows a bell-shaped curve and has certain characteristics, such as a symmetric shape, a single peak, and the mean, median, and mode all being equal. This can be visually assessed through a histogram or mathematically tested through methods such as the Kolmogorov-Smirnov test or the Shapiro-Wilk test.
Yes, the distribution of n random variables can change over time. This can be due to various factors such as changes in the underlying data, changes in the population being studied, or external factors influencing the data. It is important to regularly monitor and update the description of the distribution to reflect any changes that may occur.