A routine question from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for self-study questions.

learn more… | top users | synonyms (1)

0
votes
0answers
2 views

Forecasting a ARIMA(1,1,1) model

ARIMA(1,1,1) process with constant term $\mu$ is $X_t=\alpha X_{t-1}+\mu+Z_t+\beta Z_{t-1}$ where $Z_t$ is white noise with mean zero variance $\sigma ^2$. Find one step and two step ahead forecast ...
1
vote
0answers
6 views

Diferrencing vs Moving Average

Moving Average and differencing a series can both be used to remove seasonality. Does the difference of these two lie in the model they are used? Moving Average used in classical decomposition and ...
0
votes
1answer
32 views

Forecast error for AR and MA process

AR(p) process is denoted by: $X_t=\mu+\alpha_1(X_{t-1}-\mu)+\alpha_2(X_{t-2}-\mu)+...\alpha_p(X_{t-p}-\mu)+Z_t$ I don't understand forecast error. Let $\epsilon_{t+l}$ be the forecast error at $l$ ...
1
vote
1answer
24 views

SARIMA model equation

Can someone please tell me in the book here how is this SARIMA equation obtained? I know that AR(1)=$Y_t=\alpha_1Y_{t-1}+e_t$ Non Seasonal AR(1)=> $Y_t(1-\alpha_1B)=e_t$. My question is what ...
3
votes
0answers
26 views

Does diagnolizing higher-order cross-moment matrices lead to independent variables?

Diagonalizing the covariance matrix transforms multivariate data into uncorrelated variables, but does not make them independent necessarily. Does it follow from this that if I were to diagonalize ...
2
votes
2answers
69 views

Calculating probability mass functions with constraints from cumulative distribution

This is a self-study question. The name of the book is called: Applied Statistics and Probability for Engineers by Montgomery and Runger. This problem is on page 73. It's exercise 3-41. The entire ...
0
votes
0answers
27 views

Need to know if this is right and how to calculate this.\

I need to stat the null which I think is H0: P=124 Ha: P≠124 am I on the right track? I also have to test at a 5% significance level and show appropriate test stat a P-value. The stuff we went over ...
3
votes
1answer
84 views

Does the birth date of professional boxers matter? Prove/disprove what an astrologer might predict

As a followup to my question about the birth month of boxers, I am posing the fundamental question along with my hypothesis (testing if there is any truth to a conclusion an astrologer might make): ...
0
votes
1answer
22 views

Finding maximum likelihood estimates of parameters of multiple normal populations

I've just started studying maximum likelihood and likelihood ratio tests. I've calculated the maximum likelihood of a normal population with unknown mean and variance. However, I've been given this ...
5
votes
2answers
131 views

Statistical significance of birth month of professional boxers

I looked at the birth dates of the top 100 ranked professional boxers of all time (67 of them to be exact). 40% of them were born during certain 3 month-long time periods. If birth date of boxers ...
0
votes
0answers
23 views

What is the derivative of a matrix with respect to f? The matrix has softmax function in it

I need the derivative of W, which has the following expression. W is matrix which contains entries from softmax function. I couldn't find the derivative.
2
votes
2answers
44 views

What coefficients do I use for a binomial distribution problem?

I'm studying for an exam and my study guide explained combinations, permutations, and binomial distributions, but didn't cover much how to recognize where each comes into play in problems. I'm having ...
0
votes
0answers
4 views

Lagrange multiplier method [migrated]

I am doing some data mining algorithm self learning tutorial. I came up with a problem which I need your help to solve. In order to minimize the resource consumption, a car manufacturer considers how ...
0
votes
0answers
12 views

Derivation of the variance of the sample size in probability sampling

I am trying to understand how to derive the variance of the sample size $n$ in a random probability sample from a population of size $N$ with units $i=1,...,N$. Let $I_i$ be a random variable for $i$ ...
0
votes
1answer
55 views

Just finished Udacity Statistics course, now what?

I've just finished an introductory course in Statistics at Udacity, which I really enjoyed. I want to take this subject further, but not sure in which direction to go in now. I'd like to work more in ...
2
votes
0answers
52 views

proving regression with dummy variables gives same estimates as separate models

Let ($x_{i1}$, $x_{i2}$, ..., $x_{id}$, $y_i$), $i = 1,..., n$ be an i.i.d. multivariate sample and furthermore assume each observation belongs to one of possible $K$ categories. Assume for each ...
0
votes
0answers
15 views

Unsuccessful ML estimation of a modified Weibull model's parameters

I'm running this code in R to find the ML estimators of a modified Weibull model. ...
0
votes
0answers
22 views

C chart control limits

Can someone please help me to do this problem: A C Chart for non-conforming units is set up with lower control limit $0$ and a center line at $\bar c$. The upper control limit (UCL) for this ...
1
vote
0answers
19 views

Changing a target value that minimize the product being outside the specifications in quality control

I was doing problems in the article here. In the question on page 16 I don't understand part b) how to find a target value that minimize the product being outside the specifications. Can someone ...
2
votes
0answers
27 views

State space model with regression effects

I'm trying to show the following (exercise 3.11.4 from Durbin and Koopman (2012)): Show that the state space model defined by $$ y_t=X_t\beta+Z_t\alpha_t+\epsilon_t\\ ...
0
votes
1answer
20 views

From a normal distribution concerning tv rating to its profit distribution

I'm following a Quantitive Methods Course, we have been asked to solve 12 questions from an harvard business case concerning tv ratings. Intro: The questions: I've already answered the first 10 but ...
0
votes
0answers
22 views

Confustion about exam question

I'm preparing for an exam and I came across this question in a book. Below, I understand that we have to assumed a split plot in time analysis with 3 way factorial with 3 drug * 2 sex * 4 time levels. ...
0
votes
1answer
35 views

Independent and Identically Distributed(i.i.d.) Random Variables

The assumption that observations be i.i.d. tends to simplify the underlying mathematics of many statistical methods . However in practical applications of statistical modeling the assumption may or ...
12
votes
2answers
641 views

What is the logic behind method of moments?

Why in "Method of Moments", we equate sample moments to population moments for finding point estimator? Where is the logic behind this?
1
vote
0answers
44 views

Prove that the MLE $\hat{p}(1-\hat{p})$ is a asymptotically efficient

Consider when $X_1, ..., X_n \sim $ Bernoulli($p$). We want to estimate $p(1-p)$. Suppose $\hat{p}=\frac{1}{n}\sum_{i=1}^nX_i$. Prove that the MLE $\hat{p}(1-\hat{p})$ is a asymptotically efficient ...
0
votes
0answers
72 views

Mean and variance of ranks

Consider rank data 1 to n with two groups, n=n1+n2, how would one test the null that the two groups have equal rank distributions using MOMENTS? (Wilcoxon is not the answer) Is MLE possible to do the ...
3
votes
2answers
154 views

Assume $X\sim N(\mu,\sigma^2)$. What is the pdf of $X^3$

I have the following that is remaining unanswered and would love some help: Assume $X\sim N(\mu,\sigma^2)$. What is the pdf of $X^3$. For a large sample, $n$, what is the variance of the cube of the ...
1
vote
0answers
19 views

Confidence intervals for chi square goodness of fit

I'm having trouble figuring this out. I know that you calculate the confidence interval same as you would for a proportion, $p_i= P \pm 1.96 \sqrt{(P(1-P))/N}$, but in my notes it says: ...
1
vote
1answer
41 views

What is the expected number of coin flips, if you stop when the first coin flip is the same as the last?

In order to calculate the $\text{E}[X]$ where $X$ is the number of total coin flips, this is the approach I took: The probabilities are: $Pr(H) = p$ $Pr(T) = (1-p)$ Define indicator random ...
9
votes
1answer
103 views

Show that if $X \sim Bin(n, p)$, then $E|X - np| \le \sqrt{npq}.$

Currently stuck on this, I know I should probably use the mean deviation of the binomial distribution but I can't figure it out.
0
votes
0answers
22 views

I want prove $E[\int_{\Lambda}h(y)\mathcal M(t,dy)]=t\int_{\Lambda}h(y)\lambda_L(dy)$ and $\dots$

if $\Lambda$ is a Borel set such that $0 \notin \bar \Lambda$ Then. $$E[\int_{\Lambda}h(y)\mathcal M(t,dy)]=t\int_{\Lambda}h(y)\lambda_L(dy)$$ and $$E[(\int_{\Lambda}h(y)\mathcal M(t,dy)-t\int ...
0
votes
0answers
13 views

Develop a model from the 89 specimens that you can use to predict the group membership of the remaining 199 specimens’ [closed]

I have written some codes in R i dont know if i got it right i need your help and guilddance to go about this problem it will be due in two days time (Vole Data)- Consider the “microtus" dataset in ...
0
votes
1answer
27 views

If $X^T(t)=X(t\land T)$ is said to be the process $X$ stopped at $T$. I want prove following statment

Let $X$ be a stochastic process defined on a probability space $(\omega ,\mathcal F,P)$ endowed with a filtration $(\mathcal F)_{t \ge0}$ and let $T$ , $T^\prime$ be $\mathcal F_{t}-$stopping times. ...
4
votes
0answers
40 views

Calculating the first time a particle hits a state

Let $(X_{n})$ be a Markov chain with state space $D=(a,b,c)$ and transition matrix $$P= \pmatrix{ 0.4 & 0.6 & 0 \\ 0.5 & 0 & 0.5 \\1 & 0 & 0 \\}$$ A) Find the lim$_{n-> ...
1
vote
0answers
34 views

Calculating expectation function and covariance function

Let $E_n(t)$ denote the empirical cdf based on iid uniform $u[0,1]$ random variables $U_1,...,U_n.$ The corresponding uniform empirical process $(e_n(t),0\leq t\leq 1)$ is given by ...
4
votes
1answer
114 views

What does my ACF graph tell me about my data?

I have two datasets: My first dataset is the value of an investment (in billions of dollars) against time, each unit time being one quarter since Q1 of 1947. The time extends to Q3 of 2002. My ...
6
votes
3answers
115 views

Define the joint pmf of a particle moving randomly on a grid

A particle starts at (0,0) and moves in one-unit independant steps with equal probabilities of $\frac{1}{4}$ in each of four directions: north, south, east, and west. Let $S$ equal the east-west ...
2
votes
1answer
27 views

Find the pmf of a bivariate distribution when rolling a black and red four-sided die

Roll a pair of four-sided dice, one red and one black. Let $X$ equal the outcome on the red die and let $Y$ equal the sum of the two dice. Define the joint pmf on the space. So far I have $X = ...
2
votes
1answer
29 views

What is the definition of “population” in Case-Control Study?

Why in case-control studies, cases and non-case are taken from "Two-different Population?" Why don't they come from a single population?
4
votes
1answer
78 views

Reduce a Weibull model to an exponential one

I have this problem: Let $\ X\sim Weibull(\theta_1;\theta_2)$ with the sample: ...
3
votes
2answers
45 views

Finding sampling distribution of normal MLE and likelihood

I'm reviewing old exams in preparation for a statistics final, and I'm stuck on a particular question: Suppose that you have n independent random variables $Y_i$, with each distributed normal with ...
3
votes
0answers
21 views

Assumption about Systematic Errors

In Maronna, Martin and Yohai's Robust Statistics (2006, p.17), they describe a location model as follows. $$x_i = \mu + u_i,$$ where $x_i$ is the $i$th observation; $\mu$ is the hypothetical mean ...
1
vote
0answers
10 views

Normal Probability Plots in Excel [duplicate]

I am a student in an introductory statistics course and I am working on my project regarding number of hours I spend working my job a day. We went over normal probability plots and I am now trying to ...
0
votes
1answer
31 views

Suppose a random sample of size n=2 is generated from a $N(\mu, \sigma^2)$ population. Test the following hypothesis

This is a homework problem that I figured having someone explain and solve would be helpful. Null hypothesis $H_0:\mu =4$, $H_1:\mu \neq 4$. The sample is drawn from ${[x_1, x_2]}={[5,11]}$. Can $H_0$ ...
1
vote
2answers
65 views

Finding the distribution of $\frac{min(X,Y)}{max(X,Y)}$

Just need some hints on finding the distribution of $Z =\frac{min(X,Y)}{max(X,Y)}$ Where X and Y are iid ~ Unif(0,1). $P(Z \gt z) = P(\frac{min(X,Y)}{max(X,Y)} \gt z) = P(min(X,Y) \gt z*max(X,Y))$ ...
2
votes
1answer
65 views

Need help deriving a gibbs sampler for a normal mixture model with two components

Let $\theta_i$ be an indicator that the i-th eruption is a long eruption. (i.e. $\theta_i = 1$ if the i-th eruption is long and $\theta_i = 0$ otherwise.) Assume the following model and derive a ...
1
vote
1answer
42 views

Starting to apply theoretical “data science” learnings to real-world data sets

I've been reading a number of data science books recently (Python, R, etc), plus attempting a number of the MOOC courses, and so on, and the content is reasonably consistent: regression, ...
5
votes
1answer
40 views

Show the shortest confidence interval of a normal distribution

I'm having trouble formally showing a problem I have been given. It goes as so: Show that among all $(1-\alpha)*100$% confidence intervals of the form ...
2
votes
0answers
21 views

I want Find finite dimensional densities for an $\mathbb R^d-$ valued Gaussian process $X$with specified mean and covariance functions

Write the finite dimensional densities for an $\mathbb R^d-$ valued Gaussian process $X$with specified mean and covariance functions.