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Is the independent variable a random variable?
An independent random variable is a random variable that doesn’t have an effect on the other random variables in your experiment. In other words, it doesn’t affect the probability of another event happening. You wouldn’t expect the weight of one bag to affect another, so the variables are independent.
Is a random sample always independent?
Summary. A random sample is a sequence of independent, identically distributed (IID) random variables. The term random sample is ubiquitous in mathematical statistics while the abbreviation IID is just as common in basic probability, and thus this chapter can be viewed as a bridge between the two subjects.
Can a random variable be used to form a new distribution?
We can form new distributions by combining random variables. If we know the mean and standard deviation of the original distributions, we can use that information to find the mean and standard deviation of the resulting distribution. We can combine means directly, but we can’t do this with standard deviations.
Can you combine standard deviations with random variables?
We can combine means directly, but we can’t do this with standard deviations. We can combine variances as long as it’s reasonable to assume that the variables are independent. Make sure that the variables are independent or that it’s reasonable to assume independence, before combining variances.
Which is an example of a dependent random variable?
In Example 2, both the random variables are dependent . Thus the mean of the sum of a student’s critical reading and mathematics scores must be different from just the sum of the expected value of first RV and the second RV. But the answer says the mean is equal to the sum of the mean of the 2 RV, even though they are independent.
When do you add or subtract random variables?
Make sure that the variables are independent or that it’s reasonable to assume independence, before combining variances. Even when we subtract two random variables, we still add their variances; subtracting two variables increases the overall variability in the outcomes.