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# Geometric random variables introduction

Distinguishing between geometric and binomial random variables.

## Want to join the conversation?

• Is there an example of a case where:
1. Each trial has the same probability AND
2. Trial results are NOT independent?

I can see that there can be a case where trial results are independent with different probability, but I am just curious if the reverse is also true. • When will you make a geometric mean video??
(1 vote) • The geometric mean of a list of n non-negative numbers is the nth root of their product.
For example, the geometric mean of the list 5, 8, 25 is cuberoot(5*8*25) = cuberoot(1000) = 10.

It has been proven that, for any finite list of one or more non-negative numbers, the geometric mean is always less than or equal to the (usual) arithmetic mean, with equality occurring if and only if all the numbers in the list are the same.

Have a blessed, wonderful day!
• The video claims Y is not a binomial random variable because we can't say how many trials it might take to roll a 6. But realistically, if we roll the die, say, 80 times, the probability that we won't roll a 6 is only 0.000046%, which in any answer to a Khan Academy quiz question would be rounded to 0%. So, as long as we're willing to accept a very very small amount of uncertainty (and we all do, in every action we take), then we could "convert" this geometric random variable into a binomial random variable easily, by choosing some large number of times we are going to roll it. And in the video's example we can confidently handle Y as a binomial random variable... right? • The captions managed to incorrectly spell 'googol' lol
(1 vote) • Is it still a geometric random variable if you ask yourself how many trials will it take till you make two successes in a row?
(1 vote) • Why are the trial results independent for Y? It is "until I get a 6" so if for example I get a 6 in my first trial then I won't need to roll the dice again
(1 vote) • Can anyone explain why the answer and hint makes sense?
It seems the question hasn't mention anything about selection without replacement to me

Question: A class with 25 students randomly selects a different student each week to bring a class snack. Of the students, 8 percent have food allergies. Let T be the number of weeks until a student with a food allergy is selected to bring the snack.
Answer:T is neither type of variable.
Hint: In this situation, the students are selected without replacement from a small population, so each trial is not independent.
(1 vote) • for variable Y - the one with e # of rolls to get a 6. Would it be a binomial random variable if I change the variable to this:
1 if 6 was rolled in the 1st roll
2 otherwise

based on Sal's argument I would would say yes, because I eliminated the issue of non-fixed number of trials. It will be always 1, I would never need to try a second roll.
(1 vote) • Similarly to the one provided for the binomial random variable, what's the checklist for the geometric random varialble?
(1 vote) • A statistic known as the "number needed to treat (NNT)" comes up frequently in medical literature. It is known as the reciprocal as the absolute risk reduction. It seems like NNT would be an example of a geometric random variable. Can somebody confirm this? 