# 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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### Average number of distinct values

Let $q$ such that $q < n$. I pick at random $n$ values in $\mathbb{F}_q$. What is the average number of distinct values ? Thank you
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### Standard deviation shouldn't reduce?

I need to do a algorithm to calculate an integral via Monte Carlo Method, and for a purpose of simulation, I need to calculate the standard deviation of a sample generated in my program. My problem is ...
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### Most Conservative Estimate : $p = 0.5$

Question : An Electronics Company has just installed a new machine that makes a part that is used in clocks. The company wants to estimate the proportion of these parts produced by this ...
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### Getting the upper and lower quartiles in data with an even number of observations, or where the quartile lands on a decimal number

I want to draw a box plot, which requires that I know the median, the lower and upper quartiles, and the minimum and maximum values of my data. I understand that the quartiles are simply the value on ...
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### Statistics Sample requirements

In statistics , a sample should be random, have a sample size less than one-tenth of the population and be normally distributed for it to be viable for simple statistical analysis. I understand fully ...
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### Compare Unequal Entities

This is more of like an analytic question. It could be vague but let me try to narrow it down a little. Assuming, i am working on an analysis in primary education which include factors like ...
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### An Application of the Neyman-Pearson Lemma.

Problem: Using the Neyman-Pearson Lemma, determine the most powerful test of size $5 \%$. I know the Neyman-Pearson Lemma says that the test with the critical region  \left\{ x \in \{ 1,2,3,4 \} ...
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### How to calculate the right size for error bars

I am estimating $P(A|B)$ by random sampling. I do $N$ samples and event "$A$ and $B$" occurs $x$ times and event $B$ occurs $y$ times so my estimate of $P(A|B)$ is $x/y$. I would like to plot ...
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### Determining hypothesis test and application

I'm running into issues trying to figure out what type of test to use and whether two tailed or one tailed in different scenarios. How do you determine what to do in the scenarios presented? For ...
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### Is extra sum of squares $SSR(X_p|X_1,…X_{p-1})$ in multiple regression always positive?

An extra sum of squares $SSR(X_p|X_1,...X_{p-1})$, assuming that no pair of predictor variables are perfectly correlated, measures the marginal reduction in the error sum of squares. Eventually one ...
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### Combinatorics question - seats

In how many options can we arrange random number of men (identical men) in line of 15 chairs but: 1. 2 men can't sit next to each other. 2. next to each empty chair - there is at least one men. i can'...
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### Testing hypothesis using significance levels

A random sample of n=26 observations on escape time (sec) for oil workers in a test resulted in sample mean 370.69 and sample standard deviation 24.36. Suppose the investigators had believed a priori ...
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### Probability, Uniform Distribution.

Suppose $A$ is a random number chosen uniformly from the interval $(-5,6)$,what is the probability that the quadratic equation $x^2 + Ax + 1 = 0$, has no real root? This is my approach, Using the ...
Consider that you're tossing a coin $1000$ times. First $999$ times, it came up heads. Is it $50\%$ chance that the coin tails after $1000^{th}$ trial? Are these discrete events? Since the mean of ...
I need to program a function to calculate the critical values for the F-Distribution, I mean the values from the tables, for example $F_{1,1}(0.95) = 161.45$. I was looking in the Abramowitz & ...