# 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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### Probability of the sum of independent standard normal random variables

Let $X_1, X_2, X_3, X_4$ be independent standard normal random variables and $$Y = X_1^2 + X_2^2 + X_3^2 + X_4^2$$ Find the probability that $Y \leq 3$. For this problem I know that the ...
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### Expected distance within a distribution is smaller?

consider we have two general distributions $f_1$ and $f_2$, assume they have different support $S_1$ and $S_2$. Is the expected distance btween two points draw from the same distribution smaller than ...
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### WHY?The Squared Euclidean Imbalance are equal to Fourier coefficients

I'm reading the classical paper about distinguishing attack, How Far Can We Go Beyond Linear Cryptanalysis ,Thomas Baign`eres, Pascal Junod, and Serge Vaudenay. The only proposition I don't ...
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### What is the 'growth constant'?

I'm looking into the formula of growth, namely $$N= N_0 e^{kt}$$ where $k$ is the 'growth constant'. What is the growth constant and how do I find it? I'm looking at a bug that has on average 1,67 ...
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### What to do with the boundary values of a bin in a histogram?

Suppose I want to make a simple frequency histogram of the following data: $$\{3, 3, 4, 5, 5, 6, 7, 7, 8, 10, 11\}$$ I'm supposed to use bins of size $5$, starting with zero. Here's my question: Is ...
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### how to test a hypothesis when given population mean and standard deviation is known?

the mean weight of a 6 year old child is 49.3 lbs. another study indicated that in a sample of 196 six year olds the mean weight was 51.5 lbs. Assume a population standard deviation of 14. use the ...
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### Mean & SD of Sampling Distribution

A population consists of $4$ numbers $\{0, 2, 4, 6\}$. Consider drawing a random sample of size $n = 2$ with replacement. (a) What is the sampling distribution of $\bar x$? Is this a normal ...
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### probability question needs some help

suppose $X$ and $Y$ are independent and identically distributed random variables that are uniformly distributed on $[0,1]$ What is the PDF of $W=Y-X$ i tried to draw a picture to illustrated it ...
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### Deriving the variance of the sample mean $\mathrm{Var} (\bar{y})=\frac{1}{n}(1-\frac{n}{N})S^2$

For a population of size $N$ with a simple random sample size $n$ derive the formula $$\mathrm{Var}(\bar{y})=\frac{1}{n}\left(1-\frac{n}{N}\right)S^2$$ where $S^2$ is the population variance. Hint: ...
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### Standard deviations or two variances [closed]

Two variances or standard deviations? Listed below are the numbers of years that popes and British monarchs lived after their election or coronation.Treat the values as simple random samples from a ...
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### Finding the MLE for $θ$ given a probability density function $f(y |\theta )$.

Let $Y_1$, $Y_2$, . . . , $Y_n$ denote a random sample from the probability density function f (y | θ)=\begin{cases} (θ + 1)y^θ, & 0 < y < 1; θ > −1,\\ 0 ,& \text{elsewhere.}\end{...
I am a little bit confused when i was asked to Suppose $X_1, X_2,\ldots,X_n$ is a simple random sample from a continuous distribution with density function $f(x)$. Consider the new random variable $T$...
Suppose you have two data sets: Dataset $A$: $4$, $2$, $6$, $5$, $3$, $3$, $5$, $4$, $4$ Dataset $B$: $8$, $0$, $0$, $8$, $9$, $1$, $1$, $9$, $0$ Both data sets have a mean of $4$, but dataset $A$'...