# Tagged Questions

Questions on the Gaussian, or normal probability distribution, which may include multi-dimensional normal distribution.

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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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### norma distribution and log-normal distribution

I often see when people analyzing data, they assume data has either normal or log-normal distribution, and trying to fit data into a distribution for the convenience of data analysis (e.g. by ...
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### Show that $(\bar{X})^2$ is not an unbiased estimator for $\mu^2$

If $X_1, ... , X_n$ are $n$ identical distributed independent random variables each with mean $\mu$ and variance $1$. A little confused by this question. Is it asking for if $(\bar{X})^2$ != $\mu^2$....
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### Finding probability sample proportion is less than 33% assuming null hypothesis is true

Candidates 1,2 and 3 are running for a position in a company. Candidate 1 claims 38% favourability among all the voters. Assuming this is true, what is the probability that in a random sample of 500 ...
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### Asymptotic Moments of the Binomial Distribution, $E(X/(np))^k = 1 + O(k^2/n)$?

Let $X \sim \text{Binomial}(n, p)$ be the sum of $n$ Bernoulli($p$) random variables. What is the value of $E(X/(np))^k$, where $k$ is a large integer, as $n$ grows large? From calculations the ...
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### If Z has a normal distribution with mean 0 and variance $\sigma^{2}$, and $Y=Z^{2}$, what would the density function of Y be? [duplicate]

How would I go about finding this density function? Thanks
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### Build skew normal distribution knowing the mean, max, and min

Say I have a data point with included errors and I want to build some continuous distribution around it. Normally this might be a Gaussian because one knows the sigma and mean right off the bat. ...
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### Testing the independence of two jointly normal variables

Variables $u$ and $v$ are jointly normal, correlated with zero mean. $X$ is a linear combination of $u$ and $v$: \begin{align*} X := \frac{u}{\sqrt{E(u^2)}}-\rho\frac{v}{\sqrt{E(v^2)}} \end{align*} ...
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### Nomrmal probability distribution

A nationalised bank has found that has dialy balance available in its savings accounts follows a normal distribution with a mean of rs. 500 and standard deviation of rs. 50 The percentage of saving ...
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### Why a normal distribution would not give a good approximation to the distribution of marks

An examination is marked out of $100$. It is taken by a large number of candidates. The mean mark, for all candidates, is $72.1$ and the standard deviation is $15.2$. Give a reason why a normal ...
The Mean Absolute Deviation of the normal distribution is simply $$\sqrt{\frac{2}{\pi}}\sigma,$$ where $\sigma$ is the standard deviation of the normal distribution. (Wikipedia, Mathworld.) How do I ...