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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Can Poisson distribution be used in my example?

Lets say that I have an infinite population of individuals of finite density. The aim of the individuals is to find shelter. Density of individuals is $x$ and density of shelters is $y$. In a given ...
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1answer
68 views

Correctness of a statistical evaluation of a parameter

I have a question about a non-Gaussian distributed parameter that can only take certain values in a defined interval. Knowing that I have to define this parameter starting from a set of its values and ...
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2answers
35 views

I'm confused with one conditional probability problem

everyone! I'm confused with the definition of conditional probability. Assume we have one continuous random variable X and one discrete variable Y. I think $P(X>x|Y=y) = \int_{t=x}^\infty ...
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15 views

Correlation/Regression for Continuous and Discrete data

I want to correlate a data where one axis is continuous (ranging from 0 to 1), other axis is discrete. Discrete axis scale is 1 to 5 (1 is for Strongly Disagree and 5 is for Strongly agree). How ...
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1answer
35 views

Probability of batter getting fewer than 200 hits

A certain baseball player has a batting average $p=0.2$ (meaning that the chance of a hit is $0.2$ in each at-bat). Show that the probability of the player getting fewer than $200$ hits in his next ...
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24 views

How would one generate a set of $x$ random values conforming to a certain criteria?

I basically want to generate a set of $x$ numbers given $x$, a minimum, maximum and average. The set of numbers must conform, yielding the given average, with the smallest number being the given ...
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6 views

Proving that the Standard Sample Covariance is Biased

I know to be unbiased, the covariance should be $$\frac{1}{n-1} C_{xy}$$ but I'm trying to show how $$\frac{1}{n} C_{xy} = (n-1)C_{xy}$$ so, to do this, I reckon I'd probably go about finding ...
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2answers
39 views

Expected value for number of ties in n coin tosses?

I flip a coin $n$ times, at each toss I count how many heads and how many tails have come out so far. An example with $n=4$ might be: ...
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2answers
22 views

Hypothesis testing rejection question

If a hypothesis is rejected at the 0.025 level of significance, then it may be rejected or not rejected at the 0.01 level. Is this statement true? If it is true can you explain it to me why? I cannot ...
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1answer
30 views

Probability that hand contains Ace and King of at least one suit?

Compute the probability that a hand of 13 cards (drawn randomly from a standard deck of 52) contains both the ace and the king from at least one suit. I think I would use the inclusion exclusion ...
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18 views

How many units in production should be tested to ensure that the batch is healthy?

I have this assigment where I'm supposed to construct a test rig for plastic components due to the fact that a company that manufactures furniture has received lots of warranty issues regarding this ...
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30 views

What is the difference between weak and strong law of large numbers? [duplicate]

Why is the Weak Law and Strong Law always stated separately? From my textbook, weak law is convergence in probability and strong law is about convergence almost surely. But doesn't 'almost surely' ...
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1answer
25 views

Probability of drawing no aces with replacement of cards?

If you choose n cards with replacement (randomly choose a card, note what it is in a list, replace it in the deck, and repeat), then what is the probability that the list of cards contains no aces? I ...
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1answer
19 views

Normal distribution and two tailed tests

do we have to assume normal distribution in order for two tailed tests? Eg: According to the Australian Bureau of Statistics, the quantity of waste ending up in municipal landfills amounts to 0.80 kg ...
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1answer
23 views

One tailed or two tailed

Ok so this the question: An administrator at a medium-sized hospital tells the board of directors that, among patients received at the Emergency room and eventually admitted to a ward, the average ...
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2answers
38 views

If there is a 1 in 20,000 chance for an event every 3 seconds, what is the probability of it happening in 5 minutes? [closed]

If there is a 1 in 20,000 chance for an event, and a test is run every 3 seconds, what is the probability of it happening in 5 minutes? What is the probability of it happening in 2 hours? Thanks!
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0answers
17 views

X correlates with Y and Y correlates with Z when p-values are known

"How can I calculate the range of correlation of two variables X and Z given I have the correlations of X and Y, and Y and Z?" These are useful resources: ...
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21 views

Expected values from normal distribution

I'm stuck on a statistics question from my university past papers. The question is: The bit I'm stuck on is calculating the expected values from the truncated normal distribution So I'm really ...
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1answer
71 views

If I flip a coin $n$ times, what is the expected maximum number of heads or tails in a row?

Question: If I flip a coin $n$ times, what is the maximum number of heads or tails in a row that I should expect?
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13 views

Statistic, Hypothesis Testing

I tried to solve this problem many times but without success. Tried different tutorials still no success. Hope someone can help me. The President claims that a majority of voters are in favor of his ...
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9 views

Is there a way to calculate expected entropy and confidence bounds in this unknown multinomial parameter problem?

Given low-count and fairly low dimensional count data (non-negative integers) $n_1,\ldots,n_d$ where say $d \leq 5$ and $n_i \leq 10$, the goal is to compute the posterior mean and posterior ...
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1answer
33 views

How can I find the value z such that the event Z > z has proportion 0.08?

The variable $Z$ has a standard normal distribution. Find the value $z$ such that $85$% of the observations fall below $z$. The answer I got for that part was z = 1.04 I'm trying to figure out how to ...
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4answers
46 views

Probability that one of machines is working all 5 days

There are $2$ copy machines The probability that machine $A$ will work all day long is $P(A) = 0.9.$ The probability that machine $B$ will work all day long is $P(B) = 0.85.$ A working week is 5 ...
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33 views

what is the difference between mean error and mean absolute error?

So, if I am not wrong, the formulae for mean error (ME) and mean absolute error (MAE) are following : ME= 1/n (xi - yi) MAE= 1/n Σ |xi - yi| So, what are the major differences between two, other ...
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Categorical data analysis

Consider loglinear model for a $2\times2\times2$ table with $3$ categorical variables $X$, $Y$ and $Z$. Assume mutual independence of these $3$ variables. (a) Express the model in the form of ...
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1answer
17 views

Completion with respect a collection of measures.

Given a set of measures $\mathcal{M}$ on a measurable space $(\Omega,\mathscr{F})$, the $\mathcal{M}$-completion of $\mathscr{F}$ is defined as $$ ...
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28 views

Coalescent theory - Why are coalescent times independent?

I am reading from this book and I want to make sure I understand what is going on. What I get from the book Consider a population of $N$ individuals. The population size ($N$) is constant. select ...
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29 views

A student must answer 3 out of 5 questions on a test. In how many different ways can the student select the questions?

$_nC_r=_5 C _3=\frac{5\cdot 4\cdot 3}{3\cdot 2\cdot 1}=10$. The thing above is what our teacher put as the answer in out study guide. Anyone care to explain please?
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1answer
26 views

Why is the “wrong” interpretation of confidence intervals still seemingly correct?

According to online sources, if you are operating at 95% confidence, it means if you repeated a sampling process many times and then looked at the 95% confidence intervals over all the results, 95% of ...
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1answer
30 views

Stats: Why is this result significant but this other one not significant?

I test correlation coefficients $r$ for significant deviation from 0 using the resulting $t$ statistic. The result of two-tailed tests: $r=0.04$, $n=300$, $P=0.4900657$ (not significant) versus ...
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1answer
24 views

Assigning Weights

I am doing a small project,wherein I wish to apply weights to 6 different entities.My question is,is there any scientific/statistical method of assigning weights to an item?Any help would be ...
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1answer
41 views

Understanding of expected value with summation

I got a problem with a question. The question is as follows: There is a person that needs to open 3 locks. In total got he got 11 keys, but he forgot what key belongs to what lock, so he is going to ...
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1answer
20 views

Does scatterplot matrix “work” with quadratic variables?

basically I want to plot a scatterplot matrix using a few variables. For simplicity lets say my model is: $$z=\alpha_0 + \alpha_1w+\alpha_2x+\alpha_3y+\alpha_4y^2 + \epsilon$$ When I plot the matrix, ...
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1answer
15 views

Rayleigh Distribution - Density, Expected Value Question

This is a question on a review sheet I'm studying for. I know how to integrate by parts, but I don't know how to pull the probability function of the normal distribution. It's needed to complete this ...
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1answer
13 views

Probability of successful sampling fron a population

Say I have a list of 100 questions from which to study for an examination. In the examination I will be asked 10 random questions from the 100 and I pass the exam if I answer 6 questions correctly. ...
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2answers
27 views

Finding expectation and variance of a selection of three balls out of six?

I just asked this question, but worded it wrong so while the given answers are useful, they still leave me confused for where I am in the progression through my stats book. My problem is I've got 3 ...
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22 views

Uniform most powerful Test for one-sided hypothesis

I am trying to understand this proof above. What I am confusing is (1) The whole theorem correspond to the hypothesis $H_0:θ\leθ_0 \, vs \, H_1:θ\gtθ_0$. But at the beginning of the ...
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4answers
48 views

Probability of particular subset of balls occurring in a larger set chosen from a total?

If I have 3 balls chosen out of 6 (2 blue, 2 red, and 2 green) with replacement, what is the chance a chosen ball will be blue? How about two blue balls? I think I can reason this out, but I'm ...
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1answer
17 views

Question about law of iterated expectations?

I have this question: Let Y = a + bX + U, where X and U are random variables and a and b are constants.Assume that E(U|X) = 0, and that Var(X) > 0. I need to find E[UX] The answer is zero, found ...
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31 views

expected length of a k-dimensional normal random vector

Let $X$ is a random vector size $p$ from multivariate normal distribution $\mathcal{N}$($0$, $\sigma$ $I$), $I$ is identity matrix. I want to find the expected value of reciprocal of norm like this ...
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Is this an instance of the base-rate fallacy?

The following line of probability reasoning is supposedly fallacious, and is an instance of the base-rate fallacy. The argument is that $(1)-(3)$ don't give us enough reason to conclude that $(C)$. ...
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1answer
25 views

Distribution of Normal distribution

suppose $X \sim Normal(\mu, \sigma^{2})$. What is the distribution of $Y := N(X)$? where $N$ denotes Standard Normal Cumulative Distribution Function? e.g. in a special case when $\mu = 0$ and $\sigma ...
2
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1answer
28 views

Statistics - Book Recommendation

I am taking a course in statistics. It covers: Parameter estimations: point and interval estimations, etc. Hypothesis testing: comparison of means, comparison of probabilities, Chi square tests, ...
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1answer
32 views

Probability of two jacks drawn from a five-card draw [closed]

five cards are drawn from a pack of 52 well-shuffled cards. What is the probability that at least two jacks are obtained?
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2answers
46 views

Variance $= 0$, show that $X=\mu$ with probability one

If the variance of $X$ is zero, show that $X=\mu$ with probability one. Using Chebychev's inequality that is, \begin{equation*} P(|X-\mu|\geq k\sigma)\leq\frac{1}{k^2}, \end{equation*} I just let ...
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1answer
21 views

Repeated Permutations

In school we have been studying combinations and permutations, and in a programming assignment I was testing points on a coordinate plane. Testing all integer points surrounding the point (0,0) you ...
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21 views

Hypergeometric Distribution

Consider 12 teams of two people at a particular time, including two particular teams designated as team A and team B. Suppose that a later time six people have been promoted, and it may be assumed ...
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1answer
26 views

Interpreting Entropy

All you data scientists will probably know the entropy equation: $$H(p)=-\sum_{i=1}^{n}{{p}_{i}}\cdot\log_{2}{{p}_{i}}$$ And, using this, I was messing around with some compression, and calculated ...
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1answer
12 views

Discrepancy between different methods for finding standard deviation?

I can't see where I am going wrong. There are two different ways of writing the standard deviation: $ \sigma = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i – \overline{x})^2}$ $ \sigma = ...
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1answer
71 views

Gambling to pay off debt?

Someone told me something interesting today. They said they were going to take their bonus check from work, to the casino because they have "better odds" of paying off more debt then if they would ...