Tagged Questions

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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10 views

Dummy variable interpretation [duplicate]

I have a model $$\ln({\rm earnings}) = 2.618656-.0899657{\rm female}+.382019{\rm white}-.2754126 {\rm female}\times{\rm white} $$ Now i know there is gender pay difference with b1 (9%), I also know ...
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1answer
26 views

Dummy variable interaction regression

I have a model: $$ \ln({\rm earnings}) = a+b_1{\rm female}+b_2{\rm white}+b_3{\rm female}\times{\rm white} $$ ${\rm female}$ and ${\rm white}$ are dummy variables. I have interpreted $b_1$ and $b_2$: ...
0
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0answers
8 views

Method of moments estimate of a function of a parameter

xi's (i=1,2,3,....n) are a sample drawn from a distribution which is poisson with parameter theta find the Method of Moments and MLE estimator for P(x1+x2+x3=0)
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1answer
24 views

Interpretation of interaction term

I have a model: $$ \ln({\rm earnings}) = a+b_1{\rm female}+b_2{\rm white}+b_3{\rm female}\times{\rm white} $$ ${\rm female}$ and ${\rm white}$ are dummy variables. I have interpreted $b_1$ and $b_2$: ...
1
vote
1answer
25 views

expressing a discrete distribution as a mixture of bernoullis

How would one express a discrete distribution as a probabilistic mixture of Bernoulli random variables? An example of a discrete distribution being something like this: $P(X=1)=0.15$, $P(X=2)=0.45$, ...
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0answers
11 views

75% success, ranges for given sample sizes with 95% confidence

A given task has a 75% chance of success. With 90% confidence, what would be expected ranges of success for - 10 attempts - 50 attempts - 100 attempts - 1,000 attempts - 10,000 attempts very many ...
2
votes
2answers
50 views

Predictive with uniform likelihood

I'm trying to get a predictive density and currently getting something which I know can't be true (based on both logic and simulation based techniques. Here's the relevant information. $\theta$ is a ...
0
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0answers
14 views

Conceptual question on CRB vs SNR plot

In system identification, parameter estimation I have found in several papers that an analytical bound is derived which is the CRB of the error variance of the estimates. It is shown that the MSE of ...
5
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3answers
361 views

Using years when calculating linear regression?

I'm new to statistics, and I'm currently trying to solve an assignment for my course. The assignment is to calculate the linear regression analysis/regression equation for a data set containing ...
2
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0answers
33 views

Sum of Bernoulli random variables

I need some help with a homework assignment. The question I'm given is: "Suppose that $X_1, X_2,..., X_n, W$ are independent random variables such that $X_i\sim Bin(1,0.4)$ and $P(W=i)=1/n$ for $i=1, ...
2
votes
3answers
73 views

Probability that node A is connected to another node

Example: I have nodes A, B and C. A is connected to B and C. B is also connected to C. The link between two nodes have a probability to fail. For the link between A and B, the probability is pAB ...
0
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0answers
16 views

How to run a hypothesis test on 3 binary dummy variables?

Consider the following problem: Team A's performance (by month) in Jan-Mar is 200 and in Apr-Dec is 250. Team B's performance (by month) in Jan-Mar is 150 and in Apr-Dec. Furthermore, we know that ...
0
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0answers
20 views

Inequality of gamma distribution

Let $X_{\alpha} \sim \text{Gammma}(\alpha,1),\alpha >0$ with distribution function $G_{\alpha}$ and $X_{\beta} <_{(c)} X_{\alpha}\,\forall ~0<\alpha<\beta<\infty$. Then show ...
0
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0answers
14 views

Population proportion and confidence interval estimation

Q. A disease can be classified into four types. A random sample of size n=100 patients contains $n_1=70$ patients with type 1 disease, $n_2=10$ patients with type 2 disease, $n_3=15$ patients with ...
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0answers
52 views

Combining micro data for an econometrics paper

I am researching data for an econometrics research paper that I am doing but I am completely stuck. I am not looking for help doing the actual research, just guidance if my statistical method will be ...
0
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0answers
37 views

Stolen base success vs Independent catcher and average catcher

I would like to know if my thinking on this is correct. Note: This is not a homework or work question, I am just interested in learning about comparing averages and how it applies to the problem set ...
0
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0answers
18 views

sample size to estimate variance

I am trying to follow a thread Calculating required sample size, precision of variance estimate? and am facing difficulty understanding a step in the answer, specifically the step given below $ (n-1) ...
1
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1answer
28 views

Sample covariance mean-corrected vector proof

Prove that $$(n-1)S = X^TX -{1\over{n}}(X^T\vec1)(\vec1^TX) = X^TX-n\vec{\bar x}\vec{\bar x}^T$$ My attempt so far goes like this $$S = {1\over{n-1}}X_m^TX_m$$ Edit: Where $X_m$ is the ...
0
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1answer
36 views

“Vanilla” neural network model (Hastie et al.)

Hastie et al. (The elements of statistical learning) discuss "vanilla" neural network model on page 392. They describe the model as: Derived features $Z_m$ are created from linear combinations of ...
0
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1answer
30 views

Expectations of the geometric mean of a random sample from a uniform distribution

If I have a random sample of size n from a Uniform(0,1) and I define the geometric mean as G can anyone give me insight in to how I can find the expected value of G, E[G]? Once I can get my head ...
2
votes
1answer
23 views

Control limits in $\bar{x}$ and R chart

I am learning a Quality Control course and in theory part I don't understand calculating the control limits for $\bar{x}$ and R chart.I want to know, say when I calculate the R chart control limits no ...
1
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0answers
29 views

Solving for GLM coefficients w/ Newton-Raphson

Note : This is a question about a homework problem I am facing. I have some data that is to be modeled with a logistic regression model. I am supposed to do two things: (1) use newton-raphson ...
0
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0answers
18 views

Confidence interval for proportions for different patients

Question: Schizophrenia and other psychoses are complex and debilitating diseases, which affect about 2% of the population. Two of the approaches used, as well as in other medical diseases, to reduce ...
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0answers
30 views

two question about statistic [closed]

An elementary school discipline team is going to set a policy - students who score two or more standard deviations above the mean on a behavior problem scale will be placed into an intervention ...
1
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0answers
52 views

Incremental aggregation of statistics

I need your suggestion to solve this problem: Given a Data Warehouse with e.g. 10 million entries, additional 1000 entries arrive each day. Rather than recomputing the desired aggregates, an ...
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1answer
30 views

How to find the joint distribution in embedded space

Euclidean Embedding of Co-occurr ence Data under Section 2, the problem formulation is given. In the paper link, the Authors find the distribution for lower embedding for the squared distances between ...
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0answers
17 views

Incremental Aggregation: need some clarification [duplicate]

I have started some self study on Data mining algorithm. Recently I came accross a problem. I need your hint: Given a Data Warehouse with e.g. 10 million entries, additional 1000 entries arrive each ...
4
votes
1answer
27 views

Distribution of random sample of confidence intervals containing the true mean

Given 50 random samples, each of size 25, from a normal distribution with mean 20 and standard deviation 5. From each of the 50 samples, you can find a 90% confidence interval for the mean. Let Y be a ...
3
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1answer
61 views

You will randomly select 10 balls from the box with replacement what is $E(\bar X)$

A box contains 100 numbered balls - 21 with the number 1, 36 with the number 2 and 43 with the number 3. You will randomly select 10 balls from the box with replacement and you take the mean of the ...
1
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1answer
46 views

Expected lifetime of a device with two parts each having spares?

Consider a device with two parts : (1) and (2). Part (1) has 2 spares and part (2) has one spare. Lifetime of part (1) and its spares have iid exponential distribution with rate lambda. Lifetime of ...
4
votes
1answer
55 views

Given a chi-squared distribution, find $\Pr(\mu-2\sigma \leq Y \leq \mu + 2\sigma)$

Given a chi-squared distribution of df = 8, which R command do I use in order to find $\Pr(\mu-2\sigma \leq Y \leq \mu + 2\sigma)$? That is, the probability that $Y$ lies within 2 standard deviations ...
0
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0answers
14 views

Help finding critical on a hypothesis contrast

I´ve tried finding the variance using the moment-generating function but apparently that is not the correct method for finding the critical. Can you help me with this?
0
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0answers
24 views

Maximum Liklehood estimator of Poisson

I am trying to solve the following problem, I was able to solve first three bits of the problem but after that i am stuck and do not have clue to solve the (iv) bit. The local government has ...
0
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3answers
55 views

For Y~B(11, 0.3) what is P(|Y-5| >= 3)?

I feel this is a simple problem, yet I cannot seem to solve it. Any help is greatly appreciated.
1
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1answer
46 views

bivariate normal density function

I know how to show the first part, but I am confused about the second part, how to express the relationship between the two? Any hint, advice or suggestion is appreciated.
2
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0answers
26 views

How to determine a probability that 100% of confidence intervals from a bootstrap contain the true mean

Say I take 500 bootstraps of a population and calculate 95% confidence intervals (CIs) for each sample. I would expect that 95% of the bootstrap sample CIs to contain the true population mean. ...
1
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1answer
89 views

Mutual Exclusivity

Suppose that a study is being done on all families with one, two, or three children. Let the outcomes of the study be the genders of the children in descending order of their age. A. List sample ...
1
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0answers
67 views

Normal Distribution with mean and standard deviation

I'm trying to solve the following problem: Suppose at breast height, the diameter of trees of a particular type is normally distributed with mean=8.8 inches and standard deviation= 2.8 inches.What ...
1
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1answer
111 views

Finding the sample space of an experiment

Suppose that a study is being done on all families with one, two, or three children. Let the outcomes of the study be the genders of the children in descending order of their age. List the sample ...
1
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0answers
26 views

Probability question- From Mathematica program

Could somebody please help me, I have been trying to calculate this problem all day, but with no success. Here is the problem: "A teacher was asked by her principal to select 7 students at random ...
2
votes
1answer
35 views

Calculating the expected value and variance of an estimator of a normal quantile

I don't quite understand how to use the estimator function and the variance function and plug in the sample mean. I expected that we would plug in the value $\bar X - 1.645s$ into $E(s)$ and $V(s)$. ...
4
votes
2answers
76 views

Problem obtaining a marginal from the joint distribution

Suppose $X_1$ and $X_2$ have the joint pdf $$f_{X_1,X_2}\left(x_1,x_2 \right)=4x_1 x_2,\quad\text{for}\quad 0<x_1<1, 0<x_2<1$$ From that I found the joint pdf of $Y_1=\frac{X_1}{X_2}$ ...
0
votes
2answers
50 views

Different results from several “passes” of Random Forest on same dataset

I've been playing around with the German Credit dataset available in Kuhn & Johnson's caret package for ...
1
vote
2answers
23 views

Need help finding the probability

I have problem where you are given the number of times you must win, and the chance of winning a game. I need to find the probability that I win all 4 times. Example: I am only given two inputs, 4 ...
0
votes
0answers
42 views

Bayesian Data Analysis, 3rd edition: Problem 8.8

I'm self studying with the 3rd edition of Bayesian Data Analysis by Gelman et. al. Currently reading through Chapter 8 and trying out some of the problems. Question 8.8 has me baffled on how to solve ...
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0answers
20 views

Error in gnls step halving factor

I am getting an error running a gnls() on some data I have. I was able to converge using nlsLM(), but I ran into some autocorrelation in my errors, so I want to try to use gnls() so that I will be ...
0
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0answers
9 views

On the derivation of the closed form Yule-Walker moment estimator of a GARCH(1,1). (exercise)

The exercise states: (Yule-Walker estimator) GARCH models are typically estimated by a numerical implementation of maximum likelihood methods. This procedure has the disadvantage that it does ...
2
votes
1answer
43 views

On the Autocorrelation Matrix of an ARMA(2,2) to derive the Yule Walker Equations

For an AR(2) I can get the Yule-Walker equations: $$\begin{cases} \rho_1=\alpha_1+\alpha_2\rho_1 \\ \rho_2=\alpha_1\rho_1+\alpha_2 \\ \rho_k=\alpha_1\rho_{k-1}+\alpha_2\rho_{k-2} \end{cases}$$ ...
2
votes
1answer
46 views

Proving for an AR(2) process that $E[X_t | F_{t-1}]=E[X_t | F_{t-2}]=E[X_t | F_{t-3}]$

An exercise states: Using the law of iterated expectations applied to an AR(2) process, verify that $E_{t−k} . . . E_{t−1} (X_t ) = E(X_t |F_{t−k} ) $ for $ k = 1, 2, 3 $ where $ E_{t−k} (X_t ) = ...
1
vote
1answer
31 views

Comparing Variability

Question: Constant velocity joints (CV joints) allow a rotating shaft to transmit power through a variable angle, at constant rotational speed, without an appreciable increase in friction or play. An ...