The Normal Distribution is the distribution that results when summing up a large number of chance events.
Actually the binomial distribution describes the probability distribution that occurs when talking about chance events happening with probability p. This is a discrete distribution but for large numbers of events, it very much resembles a normal distribution and so the normal distribution is an excellent approximation to the binomial distribution and also can be used for continuous variables.
they say errors are distributed normally. what does that mean?
The binomial distribution is a pain to calculate [and indeed was difficult before computers] and so the normal distribution was found to be much easier to use [even though the formula looks a bit horrendous] because the formula does have nice mathematical properties.
The normal distribution also occurs in nature, i.e., just by measuring phenomena and plotting them (e.g. levels of insulin in men), you will more than likely see your data normally distributed.
And the normal distribution also describes the variation in data were we to repeat an experiment many times.
The normal distribution also allows one to build something called confidence intervals which is a range that is likely to contain the desired unknown estimate and a degree of confidence that the unknown estimate lies within that range (e.g., candidate will get 52% of the vote +/- 4%; so the estimate is 52% and the interval is size 8). The calculation of confidence interval assumes distribution of errors of estimation is normal and has a mean of 0. [so if I were to poll x people y # of times I wouldn't expect that I would get exactly the same result but instead the results would vary each time slightly. This would be the errors of estimation being distributed normally]
Question on memoryless property of exponential or geometric distributions:
Rolling a fair die has a uniform distribution of likely events. Rolling a 1 or a 6 or any # in between has the same probability so this is uniform. However, rolling a die until I get a 6 is memoryless, is it not? Because if I haven't rolled a 6 until time t then probability of getting a 6 when rolling it s more times (i.e., s+t) should equal the probability of just rolling it s times from the beginning yes?
Actually the binomial distribution describes the probability distribution that occurs when talking about chance events happening with probability p. This is a discrete distribution but for large numbers of events, it very much resembles a normal distribution and so the normal distribution is an excellent approximation to the binomial distribution and also can be used for continuous variables.
they say errors are distributed normally. what does that mean?
The binomial distribution is a pain to calculate [and indeed was difficult before computers] and so the normal distribution was found to be much easier to use [even though the formula looks a bit horrendous] because the formula does have nice mathematical properties.
The normal distribution also occurs in nature, i.e., just by measuring phenomena and plotting them (e.g. levels of insulin in men), you will more than likely see your data normally distributed.
And the normal distribution also describes the variation in data were we to repeat an experiment many times.
The normal distribution also allows one to build something called confidence intervals which is a range that is likely to contain the desired unknown estimate and a degree of confidence that the unknown estimate lies within that range (e.g., candidate will get 52% of the vote +/- 4%; so the estimate is 52% and the interval is size 8). The calculation of confidence interval assumes distribution of errors of estimation is normal and has a mean of 0. [so if I were to poll x people y # of times I wouldn't expect that I would get exactly the same result but instead the results would vary each time slightly. This would be the errors of estimation being distributed normally]
Question on memoryless property of exponential or geometric distributions:
Rolling a fair die has a uniform distribution of likely events. Rolling a 1 or a 6 or any # in between has the same probability so this is uniform. However, rolling a die until I get a 6 is memoryless, is it not? Because if I haven't rolled a 6 until time t then probability of getting a 6 when rolling it s more times (i.e., s+t) should equal the probability of just rolling it s times from the beginning yes?
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