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
2answers
15 views

Probability: Independent events (exactly, at most)?

we have four aunts going to a party: Albertine (0.3) Karoline (0.5) Makronelle (0.8) Petronelle (0.9) a) find the probability that exactly two of the four aunts come to the party. b) find the ...
0
votes
0answers
11 views

Discretization of the standard uniform dist.

I need some help. Sorry for the poor use of LaTEX... a) $U_{n} = \lfloor{nU}\rfloor/n$ prove that $\lim_{n \to +\infty} {U_{n}} = U$ where $U \sim unif[0,1]$ and thus that $lim_{n \to +\infty} ...
0
votes
2answers
12 views

Does it matter here that random variables are jointly distributed?

My lecture notes ask the following (true/false) question on understanding: Jointly normally distributed random variables are independent iff they are uncorrelated. I don't quite understand what ...
0
votes
0answers
10 views

Proof an edge in a geometric graph

Suppose i take two random uniformly distributed points $X_{1},X_{2}$ in $[0,1]^{2}$. In addition i connect $X_{1}$ and $X_{2}$ by an edge if $||X_{1},X_{2}||_{\infty} \leq r$ where $0<r<1$ and ...
1
vote
2answers
38 views

Showing that $-\ln{X} \sim \exp{\alpha}$ for $X \sim Beta(\alpha, 1)$

The CDF for $X \sim Beta(\alpha,1)$ is given by: $$F(x) = \frac{\int_{0}^{x}t^{\alpha-1}dt}{\int_{0}^{1} t^{\alpha-1}dt}$$ I am given to understand that $-\ln{X} \sim \exp(\alpha)$ if $\alpha > ...
0
votes
1answer
14 views

covariance matrix in bivariate distribution

I struggle to understand how exactly you get the covariance matrix in a bivariate normal distribution. The reason is probably that I have no idea how to obtain it at all. In the exercise I have I ...
0
votes
1answer
28 views

Powers of random variables always well-defined?

Given the random variable $X$, is $X^{0}$ a random variable? Can we take the expectation $E(X^{0})$? Is $X^{0}$ or its expectation defined or undefined under any conditions (say, on the sample space ...
1
vote
1answer
21 views

X and Y have same distribution. Is the distribution of X-Y symmetric to 0?

I met this question when I went through non parameter test. I know X-Y may not be 0. Like X follows standard normal. So does -X. But X-(-X)=2X. I just wonder is X-Y (the pdf, if exists) symmetric to ...
0
votes
1answer
21 views

Is there a result that the density function for $\chi^{2}$ must be related to the standard normal density?

Suppose we have a random variable $X$ with the property that $-X = X$ (in distribution) and $X^{2} = \chi^{2}(1)$? I want to be able to conclude that $X \sim N(0,1)$. The probability density function ...
1
vote
1answer
12 views

In Discriminant Analysis (SPSS), why there are F values of the canonical functions?

Recently, I read a paper in which the author uses Discriminant Analysis, here is his words: "The discriminant analysis produced three significant canonical functions (Function 1, F(18, 2130) = ...
1
vote
1answer
22 views

Which random variable distribution can be scaled towards zero mean and unit variance?

can any random variable, not necessarily normally distributed, scaled and shifted in such a way that the new mean is 0 and the new variance is 1? If not, which can? I remember hearing about ...
0
votes
0answers
14 views

How to calculate Variance if no data set is given? [on hold]

If only a sample of 100 is given and I have to calculate the variance and the range how should I calculate?
0
votes
0answers
17 views

Econometrics and Stats

Can someone please help explain this. I know the answer is a). Or provide a link with more information. The slope estimator, β1, has a smaller standard error, other things equal, if a) there is more ...
0
votes
0answers
20 views

The t-statistics

can someone please explain this further, or is there an equation. I know the answer is (c) The t-statistic is calculated by dividing a) the OLS estimator by its standard error. b) the slope by the ...
0
votes
0answers
12 views

Mean average with range of values as a value in frequency table

Preface: This is for a homework for a Psychological Statistics class, the other questions are equally badly written or worse. I'm just trying to understand if there's something I'm missing. No good ...
-1
votes
1answer
24 views

What is the probability that the lot will NOT be passed by the Inspector? [on hold]

Batteries for torch lights are packed in boxes of 10 and a lot contains 10 boxes. A quality inspector randomly chooses a box and then checks two batteries selected randomly without replacement from ...
0
votes
1answer
41 views

number of ways to seat 6 students (3 females and 3 males)

we have 3 female and 3 male students traveling to spain. On the plane we have 3 seats on each side of the gangway, kinda like this: |A B C | |D E F| a) Suppose At this point that one female sits to ...
0
votes
0answers
17 views

Calculate the mean and the variance for a random sample of 25 bivariate observations

Consider the following summary statistics taken from a random sample of 25 bivariate observations $(x_i, y_i)$, $\displaystyle\sum _{i=1}^{25} y_i = 3.26,$ $\displaystyle\sum _{i=1}^{25} y_i^2 = ...
2
votes
1answer
12 views

Beta/Dirichlet question

A generalization of the beta distribution is the Dirichlet distribution. In its bi-variate version, (X,Y) have pdf $f(x,y) = Cx^{a-1}y^{b-1}(1-x-y)^{c-1}, 0<x<1, 0<y<1, ...
1
vote
1answer
31 views

Show independence of number of heads and tails

I am independently studying Larry Wasserman's "All of Statistics" Chapter 2 exercise 11 is this: Let $N \sim \mathrm{Poisson}(\lambda)$ and suppose we toss a coin $N$ times. Let $X$ and $Y$ be the ...
0
votes
0answers
19 views

Statistics Practice Problem Help!

X and Y are discrete random variables with joint probability mass function p_xy(x,y). The conditional probability mass function of Y given X is p_y/x (Y|X). The marginal probability mass functions are ...
0
votes
1answer
23 views

Why is $E(u)=0$ when an intercept is included in OLS Estimation?

I am reading Wooldridge's graduate econometrics text. There he states that when estimating the equation $y=\mathbf{x\beta}+u$ by OLS, if an intercept (constant term) is included in your $\mathbf{x}$ ...
0
votes
0answers
15 views

Continuity of a CDF: what is wrong about my reasoning?

I want to prove that a distribution function $F$ is continuous at all points in its domain. By definition, $F$ is right-continuous, so it is enough to prove that it is left-continuous. Basically we ...
0
votes
1answer
22 views

Finding the CDF using the definition of CDF.

I am not sure how to proceed from here using strictly the definition of the CDF: Let a point be selected from the sample space $\mathcal{C} = \{c : 0 < c < 10\}$. Let $C \subseteq ...
0
votes
0answers
8 views

How to calculate the lag 1 autocovariance for the difference of two variables from the individual autocovariances of the two variables

Is it possible to calculate the auto-covariance of the difference of two variables, from the auto-covariances of two variables being differenced? I have a situation where: $Y=\beta x$ x is 3*3 ...
0
votes
1answer
15 views

Area of a one-dimensional set.

Let C be a one-dimensional set and let $\;Q(C)=\int_C e^{-x}\;dx\;$. If $\;C_1=\{x\;:0 \le \;x \le 1\}\;$ and $\;C_2=\{x\;:1 \lt \;x \le 3\}\;$ Find the $\;Q(C_1\cup C_2)\;$. My solution: ...
0
votes
0answers
18 views

How many different ways can the letters in “statistics” be arranged? [duplicate]

How many different ways can the letters in statistics be arranged?
1
vote
1answer
47 views

Birthday Problem: Big Numbers and Distribution of the Number of Samples involved in Collisions

A lot of questions about the birthday problem can be found here, but none seems to address my problem: Background I am thinking of a hash-type data structure design which accepts a certain number of ...
-1
votes
0answers
15 views

Sample datasets with known outliers for IQR, Q-test and Z-test [on hold]

Is anyone aware of a source for sample data sets with known outliers? I've been looking around for years but haven't come up with a solution, short of creating my own limited database. Sets with ...
1
vote
2answers
28 views

Probability of getting 2 matching pairs

5 dice are rolled. What is the probability of getting 2 sixes and 2 one's. My attempt: $\binom{5}{2}\times\binom{3}{2}\times(\frac{1}{6})^4\times(\frac{4}{6})$ Is this correct? Thanks
2
votes
1answer
48 views

Percentages of percentages

I do not even know how to title this question, or the name of the thing i'm looking for, but here's an example: there's N participants we'll take just three into account, but i need a formula for N ...
0
votes
2answers
48 views

conitional probability-probability this given this

According to U.S. Department of Labor employment reports,in 2010, 39.3% of jobs were classified as management, professional, and related occupations (Mgt), 14.5% were Service occupations (Svc), 23.2% ...
1
vote
1answer
21 views

The probabilities that the independent events

The probabilities that the independent events $A$, $B$, and $C$ will occur are: $\frac34$, $\frac12$, and $\frac14$. What is the probability that at least one of the three events will happen? My ...
0
votes
1answer
17 views

How can I use the Law of Iterated Expectations to answer this stats question?

A quality control plan for an assembly line involves sampling n = 10 finished items per day and counting Y, the number of defective items. Therefore, if p denotes the probability of observing a ...
0
votes
1answer
29 views

Econometrics Question

Can someone please help explain this (or provide a website link). I know the answer is (a). To decide whether or not the slope coefficient is large or small, a) you should analyze the economic ...
0
votes
0answers
23 views

OLS standard error that corrects for autocorrelation but not heteroskedasticity

Question: By mapping the OLS regression into the GMM framework, write the formula for the standard error of the OLS regression coefficients that corrects for autocorrelation but not ...
0
votes
0answers
34 views

Statistics-Conditional Probability Question

According to U.S. Department of Labor employment reports,in 2010, 39.3% of jobs were classified as management, professional, and related occupations (Mgt), 14.5% were Service occupations (Svc), 23.2% ...
0
votes
1answer
15 views

Statistical Significance Three-sided Die

I am working with a process that, on each iteration, produces either a value of -1, 0, or 1. So for all intents and purposes, we can assume I am talking about a three sided die. I would like to ...
-2
votes
0answers
17 views

Marginal and Conditional Densities? [on hold]

How do I do this? Let f(x,y) = c(x^2 - y^2)e^(-x) 0 <= x <= infinity -x <= y < x a) Find c b) Find the marginal densities c) Find the conditional densities
0
votes
1answer
24 views

Bivariate Normal question?

My teacher posted this question at the end of the class a while ago but we never ended up going back to it. My exam is soon so I was wondering if someone could help me. Consider the Bivariate Normal ...
0
votes
1answer
46 views

Combination with selective boundaries

Im in a statistics course and I am honestly quite stuck on this problem. I really would love some guidance! "A shelf contains 9 different fiction books and 6 different nonfiction books. A woman ...
-3
votes
0answers
30 views

Marginal probability mass function help! [on hold]

Practice challenge problem on practice exam. Teacher said if I could do this, then the exam should be no problem. Solution will not come out for several more days. I would like help now. X and Y are ...
-2
votes
1answer
222 views

Posterior Probability

a) Your initial belief is that a defendant in a court case is guilty with probability 0.5. A witness comes forward claiming he saw the defendant committed the crime. You know the witness is not ...
0
votes
0answers
11 views

How to find Expected Values of errors in OLS?

I am learning OLS and we are asked to show/explain whether the following statements are true or false. We are given that $\hat{U}= Y-\beta X$ and $E(U|X)=0$. I am able to do this for the first two ...
0
votes
0answers
20 views

Definition of chance [on hold]

How is a chance setup defined? Its a term I came across in a book but it was never defined. Google doesn't shed any light.
1
vote
0answers
15 views

Sum squared errors normal

Let $X_1,..,X_n$ be independent normal random variables with common variance $\sigma^2$ and means $a+bc_i$ (where $a,b,\sigma^2 $ are constants $>0$). If $s_1,s_2$ are real numbers minimizing ...
-1
votes
2answers
29 views

probability questions4 [on hold]

theres 75 students in a statistics course, by the beginning of the semester They are divided into three groups of 25 students each. There are 35 boys and 40 girls. Suppose that the group composition ...
0
votes
0answers
14 views

Probability that the uniform random variable is in Cantor set

Question : Let $U$ be a standard uniform random variable on $[0,1]$, and $C$ be the standard cantor set. find $P(U \in C)$. Is it correct to say that since $P(U = x : x \in [a,b]$) = $1/b-a$. ...
-2
votes
1answer
104 views

Probability Question!! [on hold]

A researcher is conducting a survey of county residents in a Midwestern state. Foolishly, she uses lists of registered voters as a sampling frame and randomly draws phone numbers and addresses from ...
0
votes
0answers
8 views

Knowing that the weight corresponding to the third quartile […] calculate the value of μ and the value of σ.

The weight in kg, of cubs in a year follow a standard deviation with a mean of μ and standard deviation σ. (a) Knowing that the weight corresponding to the third quartile is 21,3kg and the weight ...