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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Statistics regression problem

Suppose a regression will be fit to the n points $(x_1, y_1),(x_2, y_2), . . . ,(x_n, y_n)$ where $x_2 = x_3 = · · · = x_n$ but where $x_1 ≠ x_2$. Show that the line must pass through the point ...
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23 views

Problem of generating a standard normal distribution

The algorithm for generating a standard normal random variable $Z$ is Step 1. Generate $Y$ with an exponential distribution at rate 1; that is, generate $U$ and set $Y=-ln(U)$ Step 2. ...
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20 views

Can boosting be thought of as a genetic algorithm? [migrated]

Can boosting be classified as a genetic algorithm or as an instance of simulated annealing? Or, is it a completely different paradigm? Essentially, I'm trying to rectify discrete optimization ...
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23 views

shifted exponential distribution with inter-arrival time

Given that time interval $T^*$ in seconds between certain events has a negative exponential distribution. The instrument cannot detect intervals which are less than $\delta$ seconds. Let $T_1, ..., ...
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11 views

The autocovariance function of ARMA(1,1)

So I am reading Brockwell and Davis introduction to Time Series analysis on page 89 where he derives the ACVF of an $ARMA(1,1)$ given by: $X_t - \phi X_{t-1}=Z_t+\theta Z_{t-1}$ with ${Z_t}$ is ...
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1answer
24 views

Statistics: how to prove efficiency of a given estimator?

So the question gave D1 and D2 as unbiased, efficient and consistent estimators of δ . D3 is a new estimator which is obtained by taking a weighted average of D1 and D2 with one quarter of the weight ...
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15 views

Standard error of estimate and standard deviation of Y [on hold]

If the standard error of estimate is equal to the standard deviation of Y, what is r, a, and $\hat{Y}$?
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12 views

Product of normal densities in a Bayesian context

Two analysts, analyst A and analyst B, are interested in the probability distribution for a multivariate-normal vector $X$ with five dimensions. A estimates a density function $f_X(X=x)$ for $X$, ...
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2answers
19 views

Sample from $\mathrm{Poi}(\lambda)$. Is the following an unbiased estimator of $1/\lambda$? [on hold]

I simply don't know how to go about answering this question. I've done a good few other questions about point estimation, but I really don't know where I'm going with this one: Thanks for the help! ...
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14 views

Probability Urn with N Coins [on hold]

An urn contains N coins among which Θ of them are perfectly balanced, (the probabilities for heads and tails is 0.5), while the remaining N - Θ coins are two headed. A coin is drawn at random, it is ...
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2answers
15 views

Trouble understanding when to use ANOVA to analyse variances?

I'm having trouble knowing when to use the ANOVA method for analysing variances. For example this question: $1.$ In an investigation of the effect of large amounts of lime on marigolds, the numbers ...
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1answer
11 views

about t-statistics

good evening every body I have a question about t-statistics in first place I need to use t-statistics to estimate the population mean from a sample set, as you see I have a data set the mean and ...
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19 views

Calculating enrichment

My question concerns how enriched something is as im trying to combine several lists of uneven group size and the answer is escaping me. So basically, I have 6 groups and I want to compare them with ...
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2answers
16 views

What machine learning approach requires minimum input data to be significant enough to consider?

I have to a choose machine learning method (binary logistic, SVM, random forest, discriminant analysis, neural networks) for finding significant predictors of a disease relapse. I have sets of 70 and ...
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3answers
21 views

Standard deviation of the mean of sample data

I can't quite understand what this formula means: $$\sigma_{\overline{x}}=\frac{\sigma}{\sqrt n}$$ I know what standard deviation $\sigma$ is - it's the average distance of my data points (samples) ...
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1answer
26 views

Help please :( confidence interval of 98% and I don't understand how to solve this at all [on hold]

If the margin of error in an estimate for the mean weight of a shipment is + or -2 pounds at a confidence level of 95 percent, what will be the margin of error at a confidence level of 98 percent? Be ...
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20 views

Probability of winning a snooker-match

Suppose, a snokker match is best of $2n-1$, so the player who wins $n$ frames wins the match. Suppose, the probability for winning a frame is $p$ for player $1$. What is the probability ...
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14 views

Hypothesis testing: does it have the highest frequency?

Let's suppose, for example, that a fisherman catches $N$ fishes, with a total of $r$ different species: $E_1$, $E_2$, ..., $E_r$. The fisherman caught $O_1$ fishes of species $E_1$, $O_2$ fishes of ...
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2answers
29 views

Histogram of random numbers from normal distribution

If I generate, say, 10000 numbers from the normal distribution (in Matlab) and want to draw a histogram with 10 bins, it resembles the normal distribution pretty accurately. However, if I decide to ...
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16 views

Bayes classifier error [migrated]

I've recently been working my way through Elements of Statistical Learning and have been stuck on Exercise 7.2 for the last couple of weeks. The question states: For a 0-1 loss with $Y \in \{0,1\}$ ...
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1answer
22 views

Finding probability, piror probability, posterior probability [on hold]

Anyone help me to solve this: A survey organization randomly selects an adult Spainsh for a survey about credit card usage. Use subjective probabilities to estimate the following. 1) What is the ...
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25 views

Please help me with my statistics problem! [on hold]

Suppose before the information technology the mean weekly income of income earning citizens of USA was \$210 ($\mu$=201). Suppose the president of the USA is interested to know the impact of the ...
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14 views

limit of characteristic function Normal

I need to find the limit of the following characteristic function as $s \rightarrow\infty$ $\frac{e^{-it\frac{s}{\sqrt{s^2+s}}}}{(1-(e^{-it\frac{1}{\sqrt{s^2+s}}}-1)s)}$ The top part seems to reduce ...
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1answer
34 views

Can I perform a 2 proportion z test on this data?

I am comparing word frequencies in two corpora. I sort the words by difference of frequency across the two corpora. I take the 200 most favored words from corpus A and the 100 most favored words from ...
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1answer
6 views

What measurement should be used to determine per unit capacity of a given volume ish question

I am reselling data packages and would like to add a sense of scale to the packages. Without disputing actual numbers, an email message is between (3-20)Kbytes, a photo 270kb, a web page ...
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2answers
22 views

probability of picking up two m&ms of same color randomly

There are 3 red m&ms, 5 green m&ms, and 8 blue m&ms. If I pick two m&ms out randomly, what is the probability of me picking two m&ms of the same color? I'm not sure if this is ...
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1answer
16 views

How to plot the power of a test using R

How do you plot the power of a test using R software for a binomial distribution? Just need help with the coding
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A trace inquality for the product of symmetric PSD matrices

I'm estimating the expectation of a quadratic form, using two different estimators, and would like to compare the variances. The first is a MC estimator, and the other is the Hutchinson estimator. I ...
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2answers
24 views

Solution to a covariance problem

Roll two dice, let $X$ be their sum, and $Y$ be the second roll subtracted from the first. Compute $\text{Cov}[X,Y]$. Brute-force calculating $\text{Cov}[X,Y]=E[XY]-E[X]E[Y]$ is fairly horrible, ...
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8 views

How to show these covariance functions form a kernel? (I.e. a covariance matrix for any finite set of points)

In machine learning (specifically, Gaussian processes), a "kernel" is a two argument function such that for any set of $N$ "input points," (any $N$, any points), the $N \times N$ matrix of pairwise ...
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1answer
21 views

Standard Deviation: Population versus Sample (specific example)

So, I'm trying to use a t-test to test a hypothesis regarding information: My students were given a question in which they chose either $1, 2, 3, 4$, or $5$ to determine how much they enjoyed my ...
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6 views

Find the confidence interval of a stratified random sample

1) A report showed the number of homicides in each state. In Indiana, Ohio, and Kentucky, the number of homicides was, respectively, 380, 760, and 260. Suppose a stratified random sample with the ...
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Approximation technique when data is missing?

I am doing some statistical studies and I would appreciate some guidance to some approximation techniques when not all data is available. I have a model that takes certain input parameters (discrete, ...
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2answers
26 views

Solving the probability of independent evnts without the complement

Suppose that virus transmision in 500 acts of intercourse are mutually independent events and that the probability of transmission in any one act is $\frac{1}{500}$. What is the probability of ...
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13 views

Statistical Multiple Linear Regression Log Transformation

If for example we have a multiple linear regression as follows: $$hydrcarb=x_1+x_2tanktemp+x_3disptemp+x_4tankpres+x_5disppres+x_6tankpres^2+x_7dispres^2$$ And I am trying to do a backward ...
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Hypothesis testing with no mention of varience

In a particular village, $n=48$ children are tested to see if they have malaria. Let $X$ be the number of children who test positive and $A$ be the proportion of all children in the village with ...
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9 views

Chebyshev Inequality Error Probability

Ok so I totally dont understand this question. Normally Chebyshev ask about the probability of range/boundaries of a given mean and SD. Here we have no mean, we are asked about the probability of ...
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0answers
9 views

Right way to apply a repeated measure anova?

I'm testing peoples attention when confronted with different sensory distractions, visual only, auditory only, and visual+auditory. My hypothesis is that people attention decrease when confronted with ...
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11 views

Closed form for a Bartlett's formula for AR(2)

Consider a stationary AR(2) process $$ Y_t=\phi_1Y_{t-1}+\phi_2Y_{t-2}+e_t $$ with $e_t$'s are i.i.d. with mean $0$ and variance $1$. Let $r_s$ be the $s$-th autocorrelation ...
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1answer
36 views

Cumulative Probability Question

I'm doing this question and I'm a bit confused, I was wondering if anyone would be able to shed some light on how to do it? The question is: Find the probability that in a box of 100 light bulbs, ...
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27 views

how to prove this function is a probability measure in $U_B$

Let $(\Omega, U, P)$ be a probability space. and $B\in U$, $P(B)\gt 0$ $U_B =\{A: A=B\cap C, C\in U\}$ its class in $\Omega$ is a $\sigma$-algebra and $P_B : U_B \to \Bbb R$ $A \to ...
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2answers
19 views

Finding standard deviation from a normal distribution

This is for a homework assignment, I'm really only confused about one step within the problem though. Question: Suppose $X \sim N(400, \sigma^2)$ where $\sigma$ is the standard deviation. If we have ...
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Asymptotic distribution for two-dimensional normal distribution

Let $(X_1,Y_1), \ldots, (X_n,Y_n)$ iid with the two-dimensional normal distribution with expected value $(\mu, v$), variances $Var(X_1) = \sigma^2, Var(Y_1) = \tau^2$ and correlation $\rho = ...
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3answers
44 views

Finding a constant $ z $ such that $ P(Z \leq z) = 0.95 $ when $ Z \sim \text{N}(0,1) $.

This is for a homework assignment on normal distributions. Question: a) Find a constant $z$ such that $P(Z \leq z) = 0.95$ b) Find a constant $z$ such that $P(Z \geq z) = 0.95$ I'm having trouble ...
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What is the best way to compare different algorithms of interpolation? [on hold]

my problem, I think, quite simple, but I can't choose the best option to solve it. For some needs I have two libraries which are calculating some stuff (both calculate the same), but the differnece is ...
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1answer
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more how many different possibilities stuff in a row

There's 4 green m&m, 5 red m&m, 8 blue m&m, 10 yellow m&m. In how many ways can you line them all up in a row. I believe the answer is 25840847132100 from an online total combinations ...
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3answers
27 views

permutation question about stuff in a row [on hold]

You have 10 dogs in total, 4 of which are samoyeds, which you can't distinguish between. The other 6 are all distinct breeds. Given that, how many different possibilities can all 10 dogs be lined up ...
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1answer
33 views

Why is this correlation near-zero?

I have data pertaining to someone's willingness to buy a certain product (via survey) and whether or not they actually make the purchase. Based on the data, among the people who say they are very ...
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3answers
31 views

Conditional probability problem help

P(A)=0.1, P(A and B)=0.05, P[(not A) and (not B)]=0.55. Ask P(A given B) I don't know which formula or how do I start it, can anyone help?
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1answer
19 views

Probability of something happening exactly x times given y tries

I'm working on my stats homework, and I completely forgot how to do this. Also, we were only taught how to do it on a calculator (TI84) and I want to know how to do it without one. The problem is ...