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
1answer
26 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 ...
0
votes
1answer
7 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, ...
0
votes
0answers
16 views

Elementary statistics.

Scored on a statistics final in a large class were normally distributed with a mean of 75 and standard deviation of 6. A)Find the 40tg percentile of the scores. B)The instructor wants to give an A ...
1
vote
1answer
18 views

Independence of 3 events

The event E is independent of F and the event E is independent of G. Does it follow that E is independent of FnG? Any nice proof to show this, I can think of plenty of examples that prove it is not ...
0
votes
1answer
12 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 ...
0
votes
1answer
7 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. ...
0
votes
2answers
15 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 ...
0
votes
0answers
9 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 ...
-1
votes
0answers
10 views

General method for find a confident interval [on hold]

Using the general method for finding a confident interval. Find a shortest length $100(1-a)$% confident interval for theta based on a sample of size 1 from x having \begin{equation} ...
2
votes
4answers
36 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 ...
1
vote
1answer
11 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 ...
0
votes
0answers
19 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 ...
0
votes
0answers
9 views

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 $(C)$. ...
-1
votes
1answer
19 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 ...
1
vote
1answer
14 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, ...
-1
votes
1answer
22 views

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

five cards are drawn from a pack of 52 well-shuffled cards. What is the probability that at least two jacks are obtained?
0
votes
3answers
38 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 ...
1
vote
1answer
19 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 ...
0
votes
0answers
19 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 ...
0
votes
1answer
22 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 ...
0
votes
0answers
13 views

statistics formula for profit calculation [on hold]

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
11 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
1answer
63 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
21 views

How to find probabilities associated with a particular normal distribution [on hold]

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
2answers
31 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
1answer
29 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 ...
2
votes
0answers
31 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
20 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
19 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
35 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 ...
-3
votes
0answers
28 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
8 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
9 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
9 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
23 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
67 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
11 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
24 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
13 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
28 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
30 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
24 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
22 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! ...