Tagged Questions

In Probability and Statistics, the standard deviation of a statistical population or data set is a measure of how much variation or dispersion exists from its average value. It is defined as the square root of the variance.

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so if I have a normal distribution with z=783 cm and sigma x = 150 cm and sigma y = 50 cm can I scale these sigmas for z=950? if so how? [on hold]

so I have a problem that says if I have a plane at z=783 cm, measure the sigma (standard deviation) of the distribution in the x and y directions. from the graphs projection in the y-axis, projection ...
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I have found a question in GRE mock test which asking standard deviation. [on hold]

Random variable (X)= 0, 1 , 2, 3, 4 Relative Frequency= 0.14, 0.38, 0.10, 0.05, 0.33
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expectation and variance of an implicit estimator

Suppose the following equation holds \begin{align*} p_2=\int\limits_{-\infty}^{\Phi^{-1}(p)}\int\limits_{-\infty}^{\Phi^{-1}(p)} \frac{1}{2\pi\sqrt{1-\rho^2}}\exp\bigg({-\frac{1}{2}\frac{x^2-\rho xy+...
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Expectation and Variance of an Estimator

Imagene following equation holds \begin{align*} p_2=\int\limits_{-\infty}^{\Phi^{-1}(p)}\int\limits_{-\infty}^{\Phi^{-1}(p)} \frac{1}{2\pi\sqrt{1-\rho^2}}\exp\bigg({-\frac{1}{2}\frac{x^2-\rho xy+y^2}{...
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Is there an equation to find the standard deviation of a list deterministic-ally?

Say I have many lists of random number between 0 and 10 inclusive, and this list has 100 values. the lists will look something like this: [9 9 4 7 0 5 8 3 ... 1 9 2 5 6 6 4 2 0 1 9 8] [6 0 1 8 6 9 ...
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How do I obtain the “final” standard deviation from a series of values containing individual (also null) SD values?

I have a list of values, say: ...
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Applying delta method on euclidean distance

In order to estimate confidence interval of a k-dimension euclidean distance, I need to use delta method to estimate standard ...
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Calculating a z-score

The 2006 Statistical Abstract of the United States reports on a survey that asked a national sample of 80,000 American households about pet ownership. Suppose that one-third of all American households ...
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is the probability of having a specific pair of normally distributed variables depends only on the distance of their standard deviation from the mean

We have 2 independent random variables $a \sim N(0,1)$ and $b \sim N(0,1)$. I want a proof (or even good intuition) to show that the chance of having the pair $(a_0,b_0)$ is a function of only the ...
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Show how Gaussian with mean $\mu$ and std dev $\sigma$ is constructed.

I am a computer science student, who has recently taken an interest in data science. I've been learning about Gaussian distributions, and I've read from the documentation of the numpy python package ...
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Standard error of mean when observations are noisy

I have two observations of a normally distributed random variable: $X_1 = 0.02, \quad X_2 = 0.10$ Obviously the sample mean equals 0.06, and the standard error of the mean $(SEM)$ is equal to $0.04$....
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Significance and Poisson processes

Must I include the Poisson error on a new observation when considering whether it is consistent with a distribution? For example, the number of rain drops that fall into a cup per minute are recorded....
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Can the mean of the means of multiple sets from a single population give insight into the individual sets or the overall population?

This relates to environmental sampling: I have three composite samples consisting of nine sub-samples each collected from a waste lagoon. Assuming I treat each composite sample result as a "mean" (...
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Can I use mean and standard deviation to spot outliers?

I have a list of measured numbers (e. g. lengths of products). Of these I can easily compute the mean and the standard deviation. Now, when a new measured number arrives, I'd like to tell the ...
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How to maximize Std Dev given a range of possible values, a number of values, and a specific mean?

(I'm asking here and not stats.stackexchange because I'd like a mathematical proof of this) In this question: Prove how to maximize Standard Deviation given a certain mean $\bar{x}$ and set of values;...
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Prove how to maximize Standard Deviation given a certain mean $\bar{x}$ and set of values

I'm talking specifically of population SD, where $$s = \sqrt{ \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2}$$ I have a hunch that $s$ is maximized for a certain mean $\bar{x}$ when the values in ...
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Prove that Standard Deviation is always $\geq$ Mean Absolute Deviation

Where $$s = \sqrt{ \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2}$$ and $$M = \frac{1}{n} \sum_{i=1}^{n} |x_i - \bar{x}|$$ I came up with a sketchy proof for the case of $2$ values, but I would like ...
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Caclulate Standard Error when subtracting two effects

I am working on this issue that compares two regions with the McCrary Test (Regression Discontinuity Design). It basically measures how the density of a variable of interest develops accross a pre set ...
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Derivation of standard error of regression estimate with degrees of freedom

I am taking a course of Econometrics: I need help to understand as to how do we arrive at the formula for standard error of regression $$\hat{\sigma}^2=\frac{\sum{e_i^2}}{n-k}.$$ I understand the ...
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sample standard deviation given population standard deviation

How do you find the sample standard deviation when given the population standard deviation? What formula do you use? If you can make up an example that would be great.
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How to find the standard deviation from the given information and what is $B(0)$ equal to?

Assume that the risk free rate is $0$ and that the stock price is given by the equation $S(t)=6e^{2t+2B(t)}$ where $B(t)$ is the standard Brownian motion. Determine the price at time $0$ of the ...
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Proof that there will always be data within 1 SD

So we just started stats at school, and our teacher told us that no matter the data, no matter how distorted or weird it is, there will always be data within 1 standard deviation of the mean. Is this ...
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I have two datasets $\{10,10,2,2\}$ and $\{13,7,0,4\}$. Now, when I compute standard deviation for both the sets, I get $4$ and $4.74$ respectively. My question: what is the significance of $4.74$ or $... 0answers 21 views Questions about Ridge Regression, how to explain the penalty term? I have read the introduction of ridge regression in https://tamino.wordpress.com/2011/02/12/ridge-regression/. As we know, the equation of OLS is ∥ y − X β &#... 3answers 49 views How does using one distribution as another's sample size affect variance? How does using one distribution as another's sample size affect variance? For example, let's say I roll a 6-sided dice and record the number shown. Then, I roll 'that many' 6 sided dice more and ... 0answers 8 views Cumulative frequency curve effects on change of standard deviation Given a cumulative frequency curve . If the standard deviation is lower and median remains the same . Is it true to say that the curve will of the above statement will be steeper and pass through ... 0answers 43 views If this mean time is estimated to be in excess of 7 days, a new process will be implemented to reduce production costs. a) You have just graduated with a post graduate degree in business and have obtained a position with a large manufacturing firm. The director of marketing has asked you to estimate the mean time ... 0answers 17 views The prime minister will accept an error of$5 million in the estimate of µ.

Government officials in Canberra have recently expressed concern regarding overruns on military contracts. These unplanned expenditures have been costing Australians millions of dollars every year. ...
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How is the t-statistic computed in this context?

According to pg. 55 of Statistics in Plain English, the t-statistic for the sample mean is $$t = \frac{\bar{x} - \mu}{s}$$ where $\bar{X}$ is the sample mean, $\mu$ is the population mean, and $s$ ...
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Applications of mean and standard deviation

If I have this set of numbers: [9,7,5,5,4,4,4,2] We know that: mean = 5 variance = 4 standard deviation = 2 But is there an application/formula of standard ...
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Volatility of investment (/w currency hedging)

I´ve been trying to compute a volatility of invesment with currency hedging and I have a question. Let's take this example. We have our money in a fond copying the S&P500 index, which has 16% ...
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How is this not a counter-example to the fact that the standard deviation of a standardized random variable must be 1?

Let $X$ be a random variable that sends all members of the sample space to some constant real number $c$. Let $Z$ be its standardized counter-part. The standard deviation of $X$ is $0$, since $X$ is ...
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The aptitude test scores of applicants to a university graduate program are normally distributed with mean 500 and standard deviation 60.

The aptitude test scores of applicants to a university graduate program are normally distributed with mean 500 and standard deviation 60. a) Applicants need a test score higher than 530 to be ...