P[X>Y | X<2Y] refers to the conditional probability that X is greater than Y given that X is less than twice Y. In other words, it is the probability of X being greater than Y, given that X is in a certain range relative to Y.
iid stands for independent and identically distributed. This means that the variables X and Y are independent of each other and have the same probability distribution. This allows for certain simplifications and assumptions to be made in statistical calculations.
The conditional probability P[X>Y | X<2Y] can be calculated using the formula P[X>Y | X<2Y] = P[(X>Y) and (X<2Y)] / P[X<2Y]. This involves finding the probability of both events occurring and dividing it by the probability of X being less than 2Y.
If X and Y are not iid variables, then the calculation of P[X>Y | X<2Y] becomes more complex. The simplifications and assumptions that can be made with iid variables may not apply, and a different approach may be needed to calculate the conditional probability.
The calculation of P[X>Y | X<2Y] of iid variables has practical applications in various fields such as finance, engineering, and biology. It allows for the prediction of certain outcomes based on the relationship between two variables and can inform decision-making in these areas.