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falranger
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Homework Statement
I've still yet to learn Latex since I'm pretty good with words equation editor, so here's the question typed out in words.
Homework Equations
I really don't know what to do here.
falranger said:I did:
So what is ##\mu## the mean of?falranger said:Yeah, N is the number of trials, and n is the number of possible outcomes from each trial. and also, considering mu is also a summation, I don't really know how to calculate mu^2.
falranger said:Homework Statement
I've still yet to learn Latex since I'm pretty good with words equation editor, so here's the question typed out in words.
Homework Equations
I really don't know what to do here.
The Attempt at a Solution
Simon Bridge said:So what is ##\mu## the mean of?
falranger said:μ is supposed to be the average value of measured x.
And also, the question is given to us like that, but I understand what you mean since I do believe that's what it should be. And I've been wondering about the N and limit myself since at the end there are no N values in the expression.
Ray Vickson said:No, ##\mu## is not supposed to be the average of the measured x; it is supposed to be the mean of the distribution---given by the formula in my previous post.
Yes, there are no N values and limits in the end, because what you are being asked to show is the the large-N limit equals something, and that 'something' is just a number, not a function of N. For example, ##\lim_{N \to \infty} 1 + (1/N) = 1,## and at that point the '1' does not have any N's in it, or any 'lim', or anything like that: it is just the number '1'.
falranger said:Ok I realize this. But I'm still not sure how to move on. For one thing,
Standard Deviation in terms of Probability Function is a measure of how spread out the values of a probability function are from the mean or expected value. It is calculated by finding the square root of the variance, which is the average of the squared differences from the mean. In simpler terms, it tells us how much the values of a probability function vary from their average value.
Standard Deviation in terms of Probability Function is calculated by finding the square root of the variance. The variance is calculated by taking the average of the squared differences between each value in the probability function and the mean. The formula for variance is:
Variance = (sum of (x-mean)^2)/n
And the formula for Standard Deviation is:
Standard Deviation = square root of Variance
Standard Deviation in terms of Probability Function tells us about the spread or variability of a data set. A higher standard deviation indicates that the values in the data set are more spread out, while a lower standard deviation indicates that the values are closer to the mean. It helps us understand the distribution of the data and can be used to make predictions about the likelihood of certain values occurring.
Standard Deviation in terms of Probability Function is closely related to the Normal Distribution, also known as the Gaussian Distribution. In a Normal Distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. This is known as the 68-95-99.7 rule. The Normal Distribution is often used to model real-world data, and Standard Deviation is a key factor in understanding this distribution.
Standard Deviation in terms of Probability Function is used in hypothesis testing to assess the likelihood that a certain result could have occurred by chance. In hypothesis testing, we compare a sample of data to a known population and calculate the standard deviation of the sample. If the standard deviation is significantly different from the standard deviation of the population, it can indicate that the sample is not representative of the population and that our results may not be reliable. This helps us determine the validity of our hypotheses.