praveenraj
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Kindly assist how did we get 0.09630 and what does Yi stands for?
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basic stats
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praveenraj
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Please assist in how to find median? is there a formula (is there a way to find percentile or quartile through formula)
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praveenraj
New Member
kindly assist in the property what do you mean by pair vice covariance ? and the covariance and correaltion of a variable with itself with examples?
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Hi @praveenraj
In regard to finding the median (see https://en.wikipedia.org/wiki/Median ), I would suggest thinking of it as the 0.50 or 50th percentile or 50% quantile, just to be thinking in terms of quantiles (VaR is a just a quantile, but instead of 0.50 quantile which is the middle of the distribution, directly in the so-called body of the distribution, VaR is a quantile typically at 0.95 or 0.99). In Excel we can use =MEDIAN(), but I am not aware of a calculator function (as the series would need to be entered), but that's because we really just need to SORT the dataset to locate the median, then go to the middle! Now, that is the simple case of equally-weighted numbers, so you do want to explore the median of a discrete distribution (e.g., binomial) and, further but more advanced, the median of a continuous distributions. But as the FRM is not deeply concerned with the median, I don't think you need to go too much further than to understand how is a quantile that just happens to be in the exact middle of the distribution.
With regard to covariance properties (see https://en.wikipedia.org/wiki/Covariance#Properties ), I do recommend understanding the general covariance between two random variables (X, Y, W, V are upper case), when there are constants (notice the constants are lower case) given by cov(aX + bY, cW + dV) = ac*cov(X,W) + ad*cov(X,V) + bc*cov(Y,W) + bd*cov(Y,V) because it has multiple special cases. The reference to dice is just to use two random six-side dice as the random variables, where is a random discrete uniform variable, P(X = x) = 1/6. If they are independent, the cov(X,X) = variance(X). I hope that's a good start!
In regard to finding the median (see https://en.wikipedia.org/wiki/Median ), I would suggest thinking of it as the 0.50 or 50th percentile or 50% quantile, just to be thinking in terms of quantiles (VaR is a just a quantile, but instead of 0.50 quantile which is the middle of the distribution, directly in the so-called body of the distribution, VaR is a quantile typically at 0.95 or 0.99). In Excel we can use =MEDIAN(), but I am not aware of a calculator function (as the series would need to be entered), but that's because we really just need to SORT the dataset to locate the median, then go to the middle! Now, that is the simple case of equally-weighted numbers, so you do want to explore the median of a discrete distribution (e.g., binomial) and, further but more advanced, the median of a continuous distributions. But as the FRM is not deeply concerned with the median, I don't think you need to go too much further than to understand how is a quantile that just happens to be in the exact middle of the distribution.
With regard to covariance properties (see https://en.wikipedia.org/wiki/Covariance#Properties ), I do recommend understanding the general covariance between two random variables (X, Y, W, V are upper case), when there are constants (notice the constants are lower case) given by cov(aX + bY, cW + dV) = ac*cov(X,W) + ad*cov(X,V) + bc*cov(Y,W) + bd*cov(Y,V) because it has multiple special cases. The reference to dice is just to use two random six-side dice as the random variables, where is a random discrete uniform variable, P(X = x) = 1/6. If they are independent, the cov(X,X) = variance(X). I hope that's a good start!
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