Lecture 11/ DISCRETE DISTRIBUTIONS/ 3rd Stage / 2nd Course /2018-2019

What are Independent Random Variables?
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. For example, let’s say you wanted to know the average weight of a bag of sugar so you randomly sample 50 bags from various grocery stores. You wouldn’t expect the weight of one bag to affect another, so the variables are independent. The opposite is a dependent random variable, which does affect probabilities of other random variables. A random variable is a variable associated with an experiment, like n tosses of a coin or d draws of cards. From a (more technical) standpoint, two random variables are independent if either of the following statements are true:
1. P(x|y) = P(x), for all values of X and Y.
2. P(x?y) = P(x) * P(y), for all values of X and Y.
The two are equivalent.
The first statement, P(x|y) = P(x), for all values of X and Y, is stating “the probability of x, given y, is x.” In other words, knowing y should make no difference on the probability, x — it’s still going to be just x no matter what the value of y.
You may recognize the second statement as the fundamental counting principle , which states that if you have two independent events, multiply their probabilities together. For example, let’s say your chances of winning a prize in bingo are 1/1000 and your odds of finding a parking space right next to the bingo hall are 1/20. Your odds of finding a parking space next to the bingo hall and winning in bingo are 1/1000 * 1/20 = 1/20,000.