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
9 views

Describing statistical outliers in specification data sheets

I have an instrument that is interrogated (say) once per second to provide a data value. After reading it for (say) 1000 seconds I have a good idea of how well it performs, with Average and Standard ...
0
votes
1answer
8 views

Permutation test and p-value

I construct a permutation test in order to see If two samples come from the same distribution or not. I have two vectors $x, y$ that hold values of sampled values from two populations and the test ...
1
vote
1answer
14 views

How to find critical values for a two sample t test

How do you find the critical values for a non-pooled two sample t-distribution test? I've been searching for online notes and I've gotten the following formula: $cv=\pm t_{1-\alpha,d}$. But I'm unsure ...
0
votes
1answer
13 views

Hypothesis test on a binomial distribution

Given that I am working on a binomial distribution $\operatorname{Bin}(10,p)$ and I am trying to construct a hypothesis test for $p$. $H_0=0.5$ vs $H_1=0.55$. Assume that we want a significance ...
0
votes
0answers
7 views

Trying to find article by Tukey

I am trying to find a commonly cited paper by John Tukey published in 1960 called "A survey of sampling from contaminated distributions", from a monograph(?) called "Contributions in Probability and ...
0
votes
0answers
7 views

Statistical sample with age ranges. How to extrapolate it using the real age distribution over population.

I have a data set consisting in the classification of the numbers of suicides by age range. I want to figure out if there is or not association between the number of suicides and the age range. But, ...
-2
votes
0answers
16 views

poisson process and continuity [on hold]

This question is about poisson process and its continuity. N = (Nt)t≥0 represents a Poisson process of positive rate λ How to show the limit of P(|Nt −Ns|>ε) tends to 0 when s tends to t?
1
vote
3answers
31 views

Need explanation how we simplified expression for variance

I cannot really understand how we did simplification for our variance. Like how we got E[X^2] on the second line. Probably some algebra gaps.. but I cannot really make sense of it. Need help! Thank ...
1
vote
0answers
10 views

Help with finding an optimal bilingual skill-based routing calculation.

First time post, I'm not sure if it is in the correct forum but this seems to be as a good place to try: I was wondering if anyone out there had experience dealing with a similar issue or knew of any ...
0
votes
0answers
14 views

Show the sample mean $\mathfrak{T}_t$ converges to the population mean faster than $n^{1/3}$.

Let $\mathfrak{T}_{t}$ be an iid random variable with support $\mathfrak{T}_{t} \in [0,1]$. Prove $n^{1/3}\frac{1}{n} \sum\limits_{t=1}^{n} (\mathfrak{T}_{t} - \mathbb{E}[\mathfrak{T}_{t}] ) ...
1
vote
1answer
14 views

Combined Distribution of Random variable

How to compute $P[T1 \le T2 \le t]$ for T1, T2 is independent random variable with exponential distribution in terms of cmf, pdf of T1 and T2? Similarly for $P[T1 \le T2 \le T3.. \le t]$ ? I tried ...
0
votes
0answers
5 views

Can I use Chow test to compare stability of two structural models?

I want to compare stability of two structural models with respect to subsamples of a given set of data. Can I use chow test to do that? As I understand, chow test is usually used to tell whether the ...
0
votes
2answers
27 views

Need clarification on a passage. (Autism Prevalence) [on hold]

Passage verbatim: According to a review by Silverman et al. (2010), the incidence of autistic disorder is 0.6–1.0 percent in the population. The disorder is four times more common in males ...
0
votes
1answer
36 views

Conditional expectation of second moment given sum of iid variables.

We have $\xi_i \geq 0$, $\forall i = \overline{1,n}$ (i.i.d. variables). Assume that $S_n = \xi_1 +...+ \xi_n$. It is easy to show that $\mathrm{E} (\xi_1\vert S_n = 1) = \frac{1}{n}$. Now we want ...
1
vote
0answers
17 views

Number of lists at some Kendall-Tau distance

I'm looking for the number of ranked lists (of length $n$) that are at a given Kendall-Tau distance $d$ $(0 \le d \le \frac{n(n-1)}{2})$ from some list of length $n$ (any list, it doesn't matter from ...
0
votes
0answers
6 views

R-program CompQuadForm/sum of squares of correlated normal variables.

I am trying to use the R-program to calculated sum of squares of two correlated normal variable with non-zero means. I have used the Imhof and Davies algorithme and they work well if means equals ...
0
votes
0answers
18 views

Accounting for non-existing values in a population.

I have run into a problem representing some data. Lets say you are doing an chemical experiment 100 times. 80 times you get the data you need so you can compute standard deviation, variance, mean, ...
0
votes
0answers
28 views

Hypothesis testing - Beta coefficient

Apologies if this is trivial, just linke me somewhere. I'm currently taking statistics 101, I can't wrap my head around the hypothesis testing of coefficients. As follows, the t-test reads $$T=\frac ...
0
votes
1answer
38 views

A random sample of size 5 is drawn from the pdf $f_{Y}(y) = 2y, 0\leq y \leq 1$. Calculate $P(Y_{(1)} < 0.6 < Y_{(5)})$. [on hold]

A random sample of size 5 is drawn from the pdf $f_{Y}(y) = 2y, 0\leq y \leq 1$. Calculate $P(Y_{(1)} < 0.6 < Y_{(5)})$. (Hint: Consider the complement.) Attempt: The pdf of the largest order ...
0
votes
0answers
23 views

Which model to be used for predictive analysis [on hold]

I have a problem where i have been given set of data against month example Month | Data1 | Data2 1---------5--------5 2---------6--------7 Consider the data 1 be the temperature and data 2 be the ...
2
votes
1answer
40 views

Joint probability distribution

$Y_1$ and $Y_2$ are jointly distributed with density $f(y_1,y_2)=4y_2^2 \qquad 0 \leq y_1 \leq y_2 \leq 1$ Determine the following: $P(\text{max} \{Y_1,Y_2\} <1/2) = ...
0
votes
1answer
20 views

Given a pdf $f_{Y}(y)$ and $n$ random observations. Find probability that last observation will be the smallest number in all the sample?

Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the entire sample? attempt: ...
1
vote
0answers
66 views

$\mathsf kth$ moment of the standard deviation about the origin from a $\mathsf N(\mu,\sigma^2)$ population

Let T be the standard deviation of a random sample of size n from a $\mathsf N(\mu,\sigma^2)$ normal population. Find the $\mathsf kth$ moment of T about the origin, and state the condition for the ...
-1
votes
2answers
22 views

Probability of the highest order statistic below the population median.

What is the probability that the highest order statistic of a random sample of size n from any continuous distribution is below the median ( population median ) of that distribution.
0
votes
0answers
39 views

Presentation of 2 images in a random but counterbalanced way

Problem: For 18 trials randomly a ‘left’ labeled image or ‘right’ labeled image is shown. The first 9 trials should contain the opposite number of left images as the last 9 (a.k.a. counterbalance). ...
2
votes
2answers
25 views

do discrete probability distribution functions need a countable number of outcomes?

Everywhere I see on the internet they say that discrete probability distribution functions have a countable number of outcomes, and continuous have uncountable infinite number of outcomes. However if ...
0
votes
0answers
13 views

Unbiased Estimator and Variance in Polling

Say a pollster conducted m = 16 polls among people who voted in the 2010 presidential elections, and reports that 55% of the respondents would vote for John Smith. But the pollster did not report how ...
0
votes
0answers
8 views

Statistics matching answer check please

1.0.0968 < p-value < 0.1056 2.0.2119 < p-value < 0.2266 3.0.0278 < p-value < 0.0316 4.0.3422 < p-value < 0.3682 Possible Answers A. Ha: mu > 2.3, z* = -0.78 B. Ha: mu ...
0
votes
0answers
8 views

MSE in case of log-transformed dependent variable

Let's consider the following log-linear model: $log(Y_i) = \alpha + X_i\beta + \epsilon_i$ for i = 1, ..., N The fitted value is: $\widehat{log(Y)} = \hat{\alpha} + X\hat{\beta}$ Assuming ...
0
votes
1answer
16 views

Hypothesis testing, t procedures [on hold]

A realtor claims the mean income of households in a certain community is \$300,000. To check this claim, a potential resident samples 30 incomes of households in the community, and obtains a mean ...
0
votes
0answers
23 views

Critical values for hypothesis testing?

How do i determine the level of significance if i know the the critical values, and how do i do the opposite, on a normal distributed curve. I am asking because I am at the moment trying to calculate ...
2
votes
0answers
10 views

Non parametric estimators for noisy funcions

Suppose there is a function $f(a,b,c,\ldots)$ of $M$ variables (fixed numbers, not random variables). Add some Gaussian noise to this function: $$ g(a,b,c,\ldots) = f(a,b,c,\ldots) + ...
1
vote
0answers
32 views

A property of the hazard function of the normal distribution

I have a problem that I can't figure out. Define $$\Gamma\left(x\right):=\frac{\phi(x)}{1-\Phi(x)}$$ where $\phi(x)$, $\Phi(x)$ are the density respectively cumulative distribution function of the ...
0
votes
1answer
12 views

One-to-one correspondence between mean value and parameters

I am currently taking a course in statistics, and in this course we are considering linear models $\mu = X\beta$ where $\mu \in L$ and $L = col(X)$ is a linear subspace of $\mathbb{R}^n$, $X$ is the ...
0
votes
0answers
15 views

What is the limiting distribution of this Markov Chain?

Take a Markov Chain with state space $\left\{ 0, 1, \dots, 20 \right\}$. Then we have the rule that given $X_n$: Compute $Z = X_n + 1$ or $Z = X_n - 1$ with probability $\frac{1}{2}$ each (if the ...
-1
votes
0answers
17 views

CLT, mle, variance [on hold]

This is a practice problem that I don't know how to do. Let X_1,...,X_n be an i.i.d. sample from an exponential distribution with the density function. f(x/T) = (1/τ)*e^(-x/τ) 0<= x <= ...
0
votes
3answers
31 views

A box contains 5 yellow and 3 red balls, from which 4 balls are drawn one at a time, at random, without replacement.

A box contains 5 yellow and 3 red balls, from which 4 balls are drawn one at a time, at random, without replacement. Let $X$ be the number of yellow balls on the first two draws and $Y$ the number of ...
2
votes
0answers
13 views

Estimate of shared variance for n samples of x and y

I am performing a t-test on n different samples of both $X_1, X_2,...,X_k$ and $Y_1,Y_2,...,Y_k$. To begin with I want to assume that all 2*n samples have the same variance but that they do not have ...
1
vote
0answers
13 views

Simulate from a distribution using Metropolis-Hastings and Rejection Sampling?

We have covered the basics behind rejection sampling as well as Metropolis-Hastings from class, but I am not sure how to use the two in conjunction to solve the following problem: Given $\pi(x) = ...
1
vote
1answer
34 views

Mean of Poisson distribution

Let $X$ have a Poisson distribution with double mode at $x=1$ and $x=2$. Find $ P(x=0)$.Here is my solution... $\mu= \frac {p(2) 2!}{p(1)}$. then how can find the mean..thanks
1
vote
0answers
7 views

What is the transformation that maps a Gaussian distribution to a Beta distribution?

Suppose X is a random variable with Gaussian distribution over domain $\mathbb{R} = (-\infty, +\infty)$, with PDF function $f_X$. And Y is a random variable with Beta distribution over domain ...
1
vote
1answer
30 views

Probability of Sample Variance Given Variance

I am trying to solve a problem that I have never seen before and cant seem to find a way to solve it so any help or tips would be appreciated! Here's the Problem: Suppose a considerable amount of ...
1
vote
0answers
23 views

Let $X$ be a continuous random variable with cdf $F$. Show that $Y = F(X)$ has uniform $(0,1)$ distribution and therefore $X = F^{−1}(Y)$

Let $X$ be a continuous random variable with cdf $F$. Show that $Y = F(X)$ has uniform $(0,1)$ distribution and therefore $X = F^{−1}(Y)$. My Sol: $P(Y \leq y ) = P(F(X) \leq y) = P(F^{-1}(F(X)) ...
1
vote
2answers
33 views

Variance of two functions

I have a problem where Var(X) is given as 8100, Var(Y) is given as 10,000. Var(X+Y) = 20,000. If X is increased by 500, Y is increased by 8%, such that the new formula is X+500 +(1.08)Y. How would I ...
0
votes
1answer
12 views

AP Probability problem on independence

This is a in-class practice problem. Suppose that the probability that a person has to park illegally and that he gets a parking ticket is 0.07. Last year Sam recorded data and found that because of ...
0
votes
1answer
36 views

Shortcut to finding $E(XY)$

The question says "Find $E(Y|X)$ and hence evaluate $E(Y)$ and $E(XY)$" The joint pdf is $$f_{X,Y}(x,y)=\begin{cases} 8xy, & \text{ for } 0< y< x < 1, \\0, & \text{ elsewhere } ...
1
vote
1answer
6 views

Poisson probability statisitics

In Poisson distribution, mean of babies born w/ defect is $1$ per month. What is the probability that exactly $12$ or exactly $14$ babies will be born w/ defect in $6$ months?
0
votes
0answers
13 views

identify nature of missingness for categorical variables

could you please give me some hints for identifying the nature of missingness for categorical variables' missing value? I mean, I gave a fast search on google scholar but I didn't find anything ...
1
vote
1answer
17 views

concept of one-tailed hypothesis testing

When we assume that the null hypothesis is true in one-tailed test for mean, we assume that the population mean is equal that value indicated in the hypotheses. Why do we not assume some other value ...
1
vote
1answer
19 views

Bivariate GBM - crosscovariance

I have troubles concerning a correlated bivariate GBM with identical drift and diffusion rates. Let $dX^i_t = \mu X^i_t dt + \sigma X^i_tdW^i_t$ and $E[dW_t ^idW^j_t] = \rho_{i,j}dt$ If $X_0^i = ...