An Introduction to the Binomial Distribution
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- Опубліковано 25 жов 2013
- An introduction to the binomial distribution. I discuss the conditions required for a random variable to have a binomial distribution, discuss the binomial probability mass function and the mean and variance, and look at two examples involving probability calculations.
The estimated probability of a 90 year old Canadian male surviving for one year was taken from Statistics Canada life tables, which can be found at www.statcan.gc.ca/pub/84-537-x.... The probability given in the table is the estimated probability that a randomly selected Canadian male, given survival to his 90th birthday, survives until his 91st. I simplified this explanation a little in the example in the video.
For those using R, here is the R code to find the probabilities for the examples in this video:
Die roll example.
Finding the probability of getting exactly two fives in three rolls:
dbinom(2,3,1/6)
[1] 0.06944444
Twenty randomly sampled 90-year old Canadian males example.
Finding the probability that exactly 18 survive for at least a year:
dbinom(18,20,.82)
[1] 0.1729609
Finding the probability that at least 18 survive for at least a year:
dbinom(18,20,.82)+dbinom(19,20,.82)+dbinom(20,20,.82)
[1] 0.2747932
or
1-pbinom(17,20,.82)
[1] 0.2747932
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Hi. Thanks for the feedback. Most of my videos move at a fairly quick pace, but some are a little bit slower. I take a bit of a different approach than many others, and moving things along at a decent clip is part of that approach. My pace in this particular video is just a smidgen faster than I'm aiming for. I imagine that at some point in the not-too-distant future, we'll have full control over playback speed so it will be easy to adjust that to one's own tastes. Cheers.
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I was wondering if you could tell me why count the probability of failure too? For example, most questions ask for the probability of success but for some reason we count the failure too? Why is that?
Because you are calculating the probability of X=x, or that x is equal to exactly something. By leaving off the probability of failure, then you are essentially saying the third roll doesn't matter, it can be a success or failure. For example, in the die problem, we were looking for exactly two 5s. However, if you calculate just the probability of two successes and leave off the third roll, then you get 0.083. Now, notice that if you calculate the probability of exactly two successes and a failure you get 0.069, and if you calculate the probability of exactly three successes then you get 0.014. Adding these together you get 0.083. Therefore, if we are looking for exactly two successes and one failure, then we need to add the probability of the failure in, which in the case of the die example, gives us 0.069.
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I have just posted how to find probability using Binomial Distribution..... I hope it's helpful....
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I have just posted how to find probability using Binomial Distribution..... I hope it's helpful....
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Thanks for the feedback! Many people do find that part helpful in understanding the formula. Cheers.
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I have just posted how to find probability using Binomial Distribution..... I hope it's helpful....
so in the table at 11:40 I didnt get that. For explaining further, is it says that 6 men to survive exactly has 0 probability??
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Brilliant video, helped me a lot! But I have a question: shouldn't the probability mass be the highest on the value, which is closest to the mean (16 in this case and not 17) or is such an assumption illogical?
In other words, is there any intuition as to why 17 at 11:20 is more probable than 16?
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