Sage-Tips

How do you know if two random variables are dependent?

Two random variables are called “dependent” if the probability of events associated with one variable influence the distribution of probabilities of the other variable, and vice-versa.

Are random variables independent?

Independence of Random Variables If X and Y are two random variables and the distribution of X is not influenced by the values taken by Y, and vice versa, the two random variables are said to be independent.

How do you prove two variables are not independent?

You can tell if two random variables are independent by looking at their individual probabilities. If those probabilities don’t change when the events meet, then those variables are independent. Another way of saying this is that if the two variables are correlated, then they are not independent.

Can two random variables have exactly the same mean but come from different distributions explain briefly?

1 Answer. In short: No. There are several properties of a probability distribution that need not affect its mean and variance, but do determine its shape.

What is the difference between variable and random variable?

Variable vs Random Variable A variable is an unknown quantity that has an undetermined magnitude, and random variables are used to represent events in a sample space or related values as a dataset. A random variable itself is a function. Random variables are associated with probability and probability density function.

Is random variable discrete or continuous?

A discrete variable is a variable whose value is obtained by counting. A continuous variable is a variable whose value is obtained by measuring. A random variable is a variable whose value is a numerical outcome of a random phenomenon. A discrete random variable X has a countable number of possible values.

Can random variables with identical distribution be independent?

Thus, just getting random variables with identical distribution does not by any means guarantee that they are independent. Share Cite Improve this answer Follow answered Nov 3 ’11 at 1:42 Dilip SarwateDilip Sarwate 39.7k44 gold badges8686 silver badges192192 bronze badges $\\endgroup$ 3 4 $\\begingroup$Thanks very much for the answer.

Is it important to specify how random variables are drawn?

Since you don’t specify howthe random variables are drawn, the question has no meaning. It is the mannerof drawing that is important. Consider a neoclassical example of an urn with one ball marked $0$ and one ball marked $1$.

How do you find the distribution function for a random variable?

Distribution Functions for Random Variables. The cumulative distribution function, or briefly the distribution function, for a random variable X is defined by. F(x) P(X x) (3) where x is any real number, i.e., x .

How do you find the standard deviation of the combined distributions?

We can find the standard deviation of the combined distributions by taking the square root of the combined variances. To combine the variances of two random variables, we need to know, or be willing to assume, that the two variables are independent. For which pairs of variables would it be reasonable to assume independence?