Independent variable



Once upon a time, me and my wife want to decide who will wash the dishes after lunch. She proposed that we should toss a coin. But you already win 5 times in a row. That coin seems on your side. I said. “You have a 50% chance to win, you already lost 5 times so today you are more likely to win!” Really??

To answer it please let me introduce the second piler of statistics and probability - Independent variable.

A variable can be an object, event, idea, feeling, time period, or any other type of category you are trying to measure. Therefore an independent variable is a variable that stands alone and isn't changed by the other variables you are trying to measure. For example, whether tomorrow is raining or not has nothing to do with what you eat tonight. So whether tomorrow is raining and what you eat tonight are independent variables. Raining or not tomorrow has nothing to do with what eat tonight.

 

On the other hand, the dependent variable is something that depends on other factors. Harvest big apple depends on you water the tree on time.


For the random events, we consider they are either independent or dependent. In the statistic and probability world, the random event only has this 2 state nothing in between.


Independent variable Independent variable Independent variable Independent variable

Sounds easy? Not really. Let me tell you a true story.


One day John opened an egg. Double yolks! What a surprise. Then he opened another one. Double yolks again!! then another and another until he finished the box and realized they were all rare double yolks egg. Then he told this story to every he meet and the next day it on the news:” Family find TEN double yolks in one box - at staggering odds of a Nonillion to one”


Well, The odds of finding one of these eggs are about 1,000 to one, so theoretically the odds on finding ten in a row is a nonillion - to one. One followed by 30 zeros! 1,000,000,000,000,000,000,000,000,000,000


I know it hard to have a feeling of that big number. Let me put it that way if he can open an egg in 1 second and this event which he opened 10 double yolks egg in a row happened once 31,688,764,615,412,794,009,150 years and according to NASA our university is about

13.8 billion years old. So that is truly a staggering odds. No wonder that John did research online about what double yolks mean. Part of their research online revealed that these eggs can be a sign of either good luck or bad luck. So they decided to buy an extra lottery ticket that day. 


Ok, let clam down and rethink is that true like the news said “staggering odds of a Nonillion to one”. You know a similar thing happens before actually, it is not that rear at all. Ok, that is confusing why theoretically conclusion doesn’t match the reality? Remember we said that finding one of double yolk egg is about 1,000 to one. That seems very reasonable. Then we multiply the number because we assume the event of finding a double yolks egg is independent. That is where we get it wrong.

 

The truth is younger hens are more likely to lay double yolks egg and same age group chicken stay together in the hennery. And the supermarket sells similar eggs together. There is a number on the box, size 6 size 8, right? So once you find a double yolks egg then there will be a large chance you are going to find the next one is double yolks too. They are not an independent event at all.

 

See find out whether events are independent or not is not that easy. So be careful. If we get it wrong the conclusion could be wildly wrong like the egg example.

 

Back to the question, we asked at the beginning. First the result of toss a coin is an independent event, so no matter how many times I lost before this time I still have a 50% chance to win. Second only about 3% change to lost 5 times in a row. I have a feeling there’s something unusual about that coin. But I won’t say that to my wife. That day I toss the coin and then happily washed the dishes. 

 

FYI: Just Google “flipping coin” and you’ll get a coin-flipping tool. Is this tool can generate a random result? If you watched my video “randomness” I think you know the answer. 


  • Million: 1,000,000

  • Billion: 1,000,000,000

  • Trillion: 1,000,000,000,000

  • Quadrillion: 1,000,000,000,000,000

  • Quintillion: 1,000,000,000,000,000,000

  • Nonillion: 1,000,000,000,000,000,000,000,000,000,000

  • Decillion: 1,000,000,000,000,000,000,000,000,000,000,000

  • Googol: 1 followed by 100 zeros

  • Centillion: 1 followed by 303 zeros

  • Googolplex: 1 followed by a googol zero

 

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