Question

1. Condition for independent
random variables *​

Answer 1

Answer:

We say that X and Y are independent if P(X=x,Y=y)=P(X=x)P(Y=y), for all x,y. In general, if two random variables are independent, then you can write P(X∈A,Y∈B)=P(X∈A)P(Y∈B), for all sets A and B. ... Since X and Y are the result of independent coin tosses, the two random variables X and Y are independent.

Answer 2

Answer:

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.