Klockan3 said:Hint: If X1 is given, what is the probability that X2 is smaller for that value?
Yes, and? Having the same pdf doesn't mean that they will always take the same value which is why they are called "independent random variables".Quincy said:don't both X1 and X2 have the same pdf?...
Independent random variables are variables that have no influence on each other. This means that the outcome of one variable does not affect the outcome of the other variable.
To determine if two random variables are independent, you can use the following criteria: 1) If the variables are discrete, you can check if the joint probability is equal to the product of their individual probabilities. 2) If the variables are continuous, you can check if the joint probability density function is equal to the product of their individual probability density functions.
Independent random variables are important in statistical analysis because they allow for simpler and more accurate calculations. When variables are independent, their joint probability distribution can be easily calculated by multiplying their individual probability distributions. This makes it easier to analyze and make predictions based on the data.
No, a set of random variables cannot be partially independent. They are either completely independent or not independent at all. If even one variable in the set is dependent on another variable, then the entire set is considered dependent.
Independent random variables have no influence on each other, whereas dependent random variables do. This means that the outcome of one variable affects the outcome of the other variable. Additionally, the joint probability distribution of independent random variables can be easily calculated by multiplying their individual probability distributions, while this is not possible for dependent random variables.