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.

learn more… | top users | synonyms

0
votes
0answers
6 views

statistics formula for profit calculation

I have the following case: In my company, we have 2 components of sales : people --> direct selling done by salespersons online --> selling via internet : social media, google ads, etc. everyday, ...
0
votes
1answer
8 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 = ...
0
votes
0answers
45 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 ...
-1
votes
1answer
18 views

How to find probabilities associated with a particular normal distribution

The leaves of a particular plant are known to be normally distributed with mean 31.3 cm and standard deviation 2.8 cm. What is the probability that a leaf picked at random will be: a) less than ...
2
votes
1answer
20 views

Why does the probability of a bivariate Poisson distribution behaves like this? (see example)

I am a beginner in working with statistics and I wanted to generate a bivariate Poisson distribution $(X_1, X_2)$ and to do so, I did according to the indication found on wikipedia (bottom of the ...
0
votes
0answers
11 views

Interpreting anova results

I have a question about interpreting anova results. Lets say the author in their study expects to see that 'A' has a greater percentage then 'B'. And in their study they have found that 'A' is 70% and ...
0
votes
1answer
27 views

Hypothesis testing.

Claim: $60\%$ of the light bulb will last more than $950$ hours. To test the claim, $100$ bulbs were randomly tested and $68$ of them lasted more than $950$ hours. Can the claim be worthy vs ...
0
votes
0answers
4 views

Minimal sufficiency and UMVUE in a pseudo-Normal distribution

I already asked a(n stupid)question about this problem here thinking I wouldn't have problems to continue it but I was pretty wrong. I'm finding several more problems trying to solve it. I'll try to ...
2
votes
0answers
26 views

What is a formal definition of 'randomness'?

What is a rigorous mathematical/logical definition of 'randomness'? Under what conditions can we truthfully apply the predicate 'is random'?
0
votes
0answers
9 views

What kind of statistical test is appropriate for this?

Variable X designates a group label (group 1, group 2, etc). Each group represents an amount of time spent watching TV. For example group 1 might watch TV less than an hour a week, group 2 watches 1-2 ...
2
votes
1answer
17 views

General probability equation

I am really struggling with statistics. I am trying to come up with the basic equation/concept of calculating the probability for something. for example: I know that the probability of coming up ...
2
votes
0answers
14 views

a variant of MLE of a normal distribution

It is well-known that if we have "n" sample observations from normal distribution with unknown mean, then the sample mean would be the MLE for the mean of the normal distribution. However, let's ...
0
votes
2answers
31 views

A woman has n keys

A woman has n keys, of which one will open her door. After trying one she discards it and tries again if it does not work. What is the expected number of attempts needed? Its straight forward to see ...
-4
votes
0answers
26 views

If 1o (in 9 out of 10) equals 200 million, what is 9? [on hold]

So, if 10 = 200 million, what does 9 equal?
1
vote
0answers
5 views

Exponential Distribution Unbiased Estimate of Coefficient of Variation?

Through simulation, I've noticed that estimates of the coefficient of variation (CV) of exponentially distributed variables are biased at low sample sizes (as seen in the plot I made). I've seen an ...
0
votes
0answers
8 views

Value consideration of maximum likelihood estimation

Suppose we have a maximum likelihood estimator $\hat \lambda$ of $\lambda$: $$\hat \lambda = \frac{\sum_{i=1}^{n}X_i}{n}$$ and a parameter $\theta$ which can be expressed as: $$\theta = ...
0
votes
0answers
8 views

Generalized Likelihood Ratio and Hypothesis Testing

I somewhat understand how to do the Generalized Likelihood Ratio Test (GLR) of $H_0:\theta=\theta_0$ vs $H_a:\theta \neq \theta_0$ in that you find the ratio of the two MLEs. What I don't understand ...
0
votes
1answer
21 views

Calculating Type II error

A dean in the business school claims that GMAT scores of applicants to the school's MBA program have increased during the past 5 years. Five years ago, the mean and standard deviation of GMAT scores ...
0
votes
0answers
11 views

Is Pearon's R the same as R^2?

Is Pearson's R the same as R-Squared (or R^2)? When is it more appropriate to use one or the other? I am tracking two variables against each other so I figured Excel's ...
2
votes
1answer
57 views

Understanding of the probability

I have a problem with understanding some of my statistics homework. I hope that some of you could help me understand. In summary the question is as follows: There are 30 people in a group, which ...
0
votes
1answer
10 views

Nonparametric Skew of Data

Recently in my studies of statistics, I have come across the second skewness coefficient to determine the skewness of the set of data. The formula is given by: $$ \frac{3(\mu - \nu)}{\sigma}$$ ...
0
votes
1answer
22 views

Distribution of the sum of random variables

Let $X_{1}$,$X_{2}$,...,$X_{N}$ be a Dirac distributed (not independent) random variables. What is the distribution of $\sum_{i=1}^{N}{X_{i}}$?
0
votes
1answer
12 views

Are there any general strategies to prove $K(x,y)$ is a machine learning kernel? (I.e. always defines a covariance matrix)?

So there are certain functions of two variables such as the standard Gaussian/radial function $K(x_i,x_j) = e^{-(x_i-x_j)^2}$ which are "kernels" as machine learning calls them, meaning that for any ...
0
votes
1answer
34 views

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 ...
0
votes
1answer
27 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. ...
1
vote
0answers
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 ...
4
votes
0answers
27 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, ..., ...
1
vote
0answers
16 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 ...
1
vote
1answer
30 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 ...
-3
votes
0answers
19 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 $\hat{Y}$?
0
votes
0answers
15 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 $X$, ...
0
votes
2answers
21 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! ...
-1
votes
0answers
19 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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
0answers
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 ...
1
vote
2answers
17 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 ...
1
vote
3answers
23 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) ...
-4
votes
1answer
28 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 ...
1
vote
0answers
23 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 ...
0
votes
0answers
18 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 ...
1
vote
2answers
31 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 ...
0
votes
0answers
16 views

Bayes classifier error [on hold]

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 $Y \in \{0,1\}$ ...
1
vote
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 ...
-4
votes
0answers
26 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 ...
0
votes
0answers
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 ...
0
votes
1answer
37 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 ...
0
votes
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 ...
0
votes
2answers
25 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 ...
0
votes
1answer
19 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