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Somefantastik
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For two independent and identically distributed random variables having the exponential distribution, do they have the same lambda value, or are the lambda values different?
Independent identically distributed (iid) random variables are a set of variables that are statistically independent and have the same probability distribution. This means that the outcome of one variable does not affect the outcome of another, and each variable has the same likelihood of occurring.
Iid random variables are commonly used in hypothesis testing and statistical modeling. They allow for simplification of complex data sets and make it easier to draw conclusions and make predictions.
The identically distributed aspect ensures that all variables have the same probability distribution, making it easier to compare and analyze them. This is important in statistical analysis as it allows for fair and accurate comparisons.
Iid random variables can be generated through simulations or obtained from real-world data sets. They can also be mathematically defined using specific probability distributions, such as the normal distribution.
One of the main assumptions when using iid random variables is that they are truly independent and identically distributed. In real-world data, this may not always be the case, which can lead to biased or inaccurate results. Additionally, depending on the specific probability distribution used, the variables may have certain limitations and may not accurately represent the entire population.