# Tagged Questions

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis.

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### Hypothesis testing for variance when the mean is not known

The sugar content of the syrup in canned peaches is normally distributed. A random sample of n = 10 cans yields a sample standard deviation of S(10) = 4.8 milligrams. Suppose that the variance is ...
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### Numerical stochastic ODE: finding E[X(t)] etc at discrete points

So if this is trivial, please tell me I'm an idiot. I guess, given a continuous time stochastic process, one can numerically approximate it at discrete points. Nothing too extreme. I'm new to this ...
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### Joint moment generating function problem

X and Y have the following joint moment generating function: $M_{X,Y}(a,b) = \Large \frac{4}{5}[\frac{1}{(1-a)(1-b)}+\frac{1}{(2-a)(2-b)}]$ Find E(XY) I have gone through this problem several times,...
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### $(Y_i - \hat{Y}_i)(\hat{Y}_i - \bar{Y}_i) = 0$

$(Y_i - \hat{Y}_i)(\hat{Y}_i - \bar{Y}) = 0$ in the image below (third and fourth line of the proof!). Why?
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### Advice on picking the best 3-set of ingredients based on their rating against different recipes

Statistics are as easy to get wrong as crypto so I thought I'd ask here rather than stackoverflow. I have some data as follows: a bunch of Xs (let's call them ingredients) are being rated by a bunch ...
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### testing correlation coefficient in a bivariate normal distribution

How can I show that $\dfrac{\hat{\rho } \sqrt{N-2}}{\sqrt{1-\hat{\rho}^2}}$ has a t-student distribution with $N-2$ degrees of freedom. I think I have to write it as a quotient of a normal $(0,1)$ ...
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### Prove $\mathsf E^Y \mathsf E^Y [X] = \mathsf E^Y [X]$

Prove that$$\mathsf E^Y \mathsf E^Y [X] = \mathsf E^Y [X]$$ by using $$\mathsf E^{Y=y} [X] = \int x\,p(x\mid y)\operatorname d x$$ or $$E^{Y=y} [X] =\sum_x x\,p(x\mid y)$$ I am having trouble on ...
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### The four assumptions on linear regression

It is clear that the four assumptions of a linear regression model are: Linearity, Independence of error, Homoscedasticity and Normality of error distribution. My question is does any of these four ...
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### Distribution of quotient of random variables

If $X$ and $Y$ are independent random variables such that $X\sim \Gamma(a,b)$ and $Y\sim\Gamma(a,c)$. What is the distribution of random variable $\frac{Y}{X+Y}$? Any help with this ?
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### Estimators in the case of refression with normally distributed errors

How can it be shown that the Maximum Likelihood Estimator and the Least Squares Estimator are equvalent in the case regression with normally distributed errors? Any help will be appreciated! Thanks in ...
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### Probability of a difference dependent samples, normal distribution but unknow parameters

I have two samples, $X_0, Y_0$, containing the marks in a test before and after training course over the same workers, thus dependent paired samples. X, Y can be considered Normal, with the same ...
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### What does ${50}\choose{4}$ mean in statistics?
I have a test tomorrow in statistics and was wondering what the following means? $$\binom{50}{4}$$ My professor along with most of my classmates have a calculator they can just plug that into. The ...