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.

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6 views

Need help with calculating this problem not sure where to start

To determine the main cost of groceries in the area an identical grocery cart of food is purchases at a random sample of 20 stores. The 20 grocery totals before tax are recorded and a 95% interval for ...
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0answers
16 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.
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2answers
37 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 ...
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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 ...
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0answers
10 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 $i$ ...
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27 views

Probability question trying to calculate need help

Suppose that the average pop song length in America is 4 minutes with a standard deviation of 1.25 minutes. It is known that song length is not normally distributed. What is the probability that a ...
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1answer
48 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
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0answers
42 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 ...
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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. ...
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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 ...
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0answers
18 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
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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\\ ...
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1answer
19 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 ...
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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. ...
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1answer
31 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 ...
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2answers
592 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?
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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 ...
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0answers
69 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 ...
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2answers
147 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 ...
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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: ...
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1answer
38 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 ...
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1answer
97 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.
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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 ...
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0answers
13 views

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

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 ...
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1answer
26 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. ...
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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-> ...
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33 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 ...
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1answer
108 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 ...
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3answers
114 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
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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 = ...
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1answer
28 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?
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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: ...
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2answers
44 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 ...
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0answers
19 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 ...
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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 ...
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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 $H_0$ ...
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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). $P(Z \gt z) = P(\frac{min(X,Y)}{max(X,Y)} \gt z) = P(min(X,Y) \gt z*max(X,Y))$ ...
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1answer
64 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 ...
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0answers
15 views

Exponential density of a battery life [closed]

So I have a homework assignment, where I'm given the exponential density of a battery life, in hours $f(x)=0.18e^{-0.18x}$ and I need to find the probability that k batteries are still running after 5 ...
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1answer
41 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, ...
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8 views

If the random variable Z is the standard normal score, which of the following probabilities [closed]

If the random variable Z is the standard normal score, which of the following probabilities could be determined without referring to a table or a computer? a.P(Z>2.86) b.P(Z<0) c.P(Z<-1.82) ...
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1answer
37 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 ...
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0answers
20 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.
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1answer
25 views

How to Get this Confidence Interval

One example in Maronna, Martin and Yohai's Robust Statistics (2006, p.2) is as follows. Given 24 measurements of certain quantity (see below) and their sample mean 4.28 and sample standard variation ...
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1answer
55 views

Is $X_{(1)} + X_{(n)}$ a good estimator for $\theta$?

Problem 8.7 From Van der Vaart's Asymptotic Statistics: Given a sample of size $n$ from the uniform distribution on $[0,\theta]$, the maximum $X_{(n)}$ of the observations is biased downwards. ...
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1answer
33 views

Stochastic Processes

I have a couple questions about stochastic processes. My professor didn't really give in depth explanations and non of his lecture slides do much explaining either. Say S(x) is a stochastic variable ...
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0answers
16 views

Need help understanding hypothesis tests in multivariate statistics

I'm not really sure where to begin with this question, and I'm not sure if I am supplying all the resources necessary to answer this question, so just let me know and I will update. I'm going to copy ...
3
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2answers
79 views

How do i derive the joint probability distribution table of X and Y?

If there is a bag with 3 red balls, 2 blue balls and 1 white ball. Two balls are drawn without replacement. Let X be number of red balls drawn and Y be number of blue balls drawn.
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1answer
114 views

What is the correlation between X and X+Y?

If $X$ and $Y$ are two random variables, how do I calculate the correlation of $X$ and $X+Y$ in terms of $\rho$, $σ_x^2$ and $σ_y^2$ given that the $\text{Variance}(X)= σ_x^2$ and ...