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# Binomial variables

An introduction to a special class of random variables called binomial random variables.

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• why is the probability of getting heads 0.6 and not 0.5?
• Not all coins are "fair". An example of an unfair coin is one that has two heads; another might be one that is weighted to fall on heads more frequently than tails.

I believe Sal's point to introducing a coin with P(heads)=0.6 is to start viewers out with the idea of trials having a successful or failed outcome that is easy to understand (lots of videos with flipped coins) and is also in keeping with random variables' outcomes having different probabilities.
• Aren't the probability of success is constant, and being independent trials the same ?
• No.

Say you have 2 coins, and you flip them both (one flip = 1 trial), and then the Random Variable X = # heads after flipping each coin once (2 trials).
However, unlike the example in the video, you have 2 different coins, coin 1 has a 0.6 probability of heads, but coin 2 has a 0.4 probability of heads. This WOULD satisfy the requirement of the trials being independent, but not the requirement of the probability of success being the same for each trial.

Hope this helps!
• What does the condition 'finite number of independent trials' mean?
• This means that the number of trials is finite (instead of infinite), and the results of any trials do not affect the success probabilities for other trials.

Have a blessed, wonderful day!
• It is not true when he says "If I get a king that looks like that would be a success. If I don't get a king that would be a failure. So it seems to meet that right over there." because there is chances that both the cards that he picks up are kings. There aren't two possible outcomes there are three possible outcomes:
⚫ 0 kings are picked
⚫ 1 king is picked
⚫ 2 kings are picked
• I was thinking the same while watching the video. For me, the way the random variable was defined does not satisfy that condition. But I guess we can always define a success event as either getting a king or two kings, and the other two outputs as failure.
• Should Y be considered a binomial variable (even without replacement) beause of the "10% Rule" for assuming independence between trials? There is a related video where the 10% rule is explained.
• Doesn't `Point1` imply `Point4` ? Or am I missing out on some kind of explicit nuance?

For example, in Sal's first coin example, isn't the possibility of someone replacing coins (which will affect the constancy of the probability of each trial) a form of dependence?
• Same as what I replied to Mohamed, No.

Say you have 2 coins, and you flip them both (one flip = 1 trial), and then the Random Variable X = # heads after flipping each coin once (2 trials).
However, unlike the example in the video, you have 2 different coins, coin 1 has a 0.6 probability of heads, but coin 2 has a 0.4 probability of heads. This WOULD satisfy the requirement of the trials being independent, but not the requirement of the probability of success being the same for each trial.

Hope this helps!
• For a variable to be binomial, does each trial need to have the same probability of success, or is it enough that each trial has an independent constant probability of success? In other words, if I flip two coins in succession, the first one fair and the second one unfair, would that qualify as a binomial variable or not?