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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3
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1answer
43 views

Proof/Derivation of Residual Sum of Squares (Based on Introduction to Statistical Learning)

On page 19 of the textbook Introduction to Statistical Learning (by James, Witten, Hastie and Tibshirani--it is freely downloadable on the web, and very good), the following is stated: Consider a ...
0
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0answers
10 views

Time delay embedding

TIme delay embedding theorum given by Takens says that from a time series of a single variable $x(t)$ we can contruct multiple vectors and is given by the formula $X(t_i) = [x(t_i),x(t_i+ ...
1
vote
1answer
16 views

Out-of-sample vs. test set

Someone asked me if I did out-of-time testing (which I assume is just out-of-sample testing but with a timeline element). But if I have a test set, is that not essentially the same as out-of-sample ...
0
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0answers
5 views

Intuition related to standard deviation as threshold

I have a set of input output training data, few samples are Input output [1 0 0 0 0] [1 0 1 0 0] [1 1 0 0 1] [1 1 0 0 0] [1 0 1 1 0] [1 1 0 1 0] and so on. I ...
0
votes
1answer
19 views

Trying to figure out a formula and answer to probability question

If I go to a certain establishment 12 times in one year (let's just say once a month), and there's a 6.25% chance each time that I go in there that I would run into a person I know, what is the ...
1
vote
1answer
28 views

Is it necessary to plot histogram of dependent variable before running simple linear regression?

I was working on an assignment. The data set was really simple, only consisting one independent variable $y$ and dependent variable $x$. Someone suggested me plot a histogram of $y$ before running ...
0
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1answer
25 views

Conceptual question on optimization

What is the intuition and the physical meaning of the mathematical expression in convex optimization? When using optimization algorithms like particle swarm or genetic algorithm, do they have ...
4
votes
2answers
177 views

What are the properties for independence

For 2 variables to be independent of each other, should the correlation = 0 or mutual information = 0 or covariance = 0. I have seen different conditions and all these are really confusing.
2
votes
1answer
78 views

Why do we prefer white noise and iid property?

EDIT When we add noise to system we say it is white noise. White noise will have a constant power spectral density, flat power spectrum. But what is the advantage of this? Why do we need iid ...
0
votes
1answer
32 views

Difference between estimation and learning

What is the difference between parameter estimation which includes system identification and learning in machine learning perspective? Let say the model is y= Ax. x is the input and y is the output. ...
0
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0answers
21 views

Neural network and dynamical system

Dynamical systemsare those whose evolution can be described by a rule, evolves with time and is deterministic. In this context can I say that Neural networks have a rule of evolution which is the ...
1
vote
0answers
52 views

Joint posterior HPD region for the coefficients of the normal linear model

This problem appear in an exam put by Chris Sims (3): http://sims.princeton.edu/yftp/emet04/ConfidenceCredibilityEx.pdf Suppose the following model: $y=\beta_1 +\beta_2 X_2+\beta_1 X_3 +\epsilon$ ...
4
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0answers
76 views

$E[e^{cX}]$ where $c < 0$ and $X$ is lognormally distributed

I am trying to calculate the expectation $$E[e^{cX}]$$ for arbitrary $c<0$ (for $c>0$ the expectation is infinite) if $X$ is lognormally distributed, i.e. $\log(X) \sim N(\mu, \sigma)$. My idea ...
0
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0answers
19 views

How to normalize time series?

This is a general question on normalization of data so that all the variables are within the same range. Why do we normalize data in pattern classification? How to normalize time series which is ...
1
vote
1answer
28 views

Implication of mutual information

EDIT For two signals or random variables to be independent, the mutual information (MI) must be zero. Let, $error = X -Y$ where X is the desired signal and Y is the measured signal. It is desired ...
0
votes
0answers
15 views

probability with permutation combination- 9 speakers in a conference on careers [on hold]

There is a conference on careers and 9 speakers from different professions will be there Determine the probability that the hockey player speaks the first and the astronaut the last. Determine the ...
0
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0answers
15 views

Confusion regarding concept of entropy and information [duplicate]

In general, entropy of a signal or image conveys the uncertainty and it is a measure of impurity. Information on the other hand tells us about how certain we are about the data. It is a measure of ...
0
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0answers
18 views

Out-of-time testing (basic question)

I understand the importance of out-of-sample testing, but could you tell me why I should (or shouldn't) do out-of-time testing ? The only use that comes to mind is if the predictive model applies to ...
2
votes
1answer
35 views

Conceptual question on mutual information and entropy

In respect to parameter estimation using information theoretic concepts, a signal X = S+N where S is the desired signal whose parameters we wish to estimate and N is the noise. The paper ...
3
votes
2answers
31 views

Negating conditional probability

I'm refreshing on bayes theorem and conditional probability and I ran across these practice problems. I was trucking along until problem 9, which states: ...
1
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1answer
28 views

Conceptual questions on Entropy and estimation

Learning Informative Statistics: A Nonparametric Approach paper presents an approach to parameter estimation by entropy minimization. There are other related works "Minimum-entropy estimation in ...
3
votes
2answers
57 views

If $X \sim$ unif$(0,1)$, what is the distribution of $U=\max \{X,1-X \}$?

Let $X$ be uniformly distributed in $(0,1)$ and set $U=\max \{X, 1-X\}$. How can I find the distributiopn of $U$? My first thought was to consider this a mixture distribution problem and use the CDF ...
1
vote
1answer
28 views

Differentiating Shannon's entropy [closed]

Can somebody please show the steps of how differentiation of Shannon's entropy yields the following result? $H = -\sum_{l=0}^{L-1} p(l)\log_2[p(l)]$ The result of differentiating is $H_m = ...
1
vote
0answers
16 views

Two-tailed test [duplicate]

In one-tailed test , we give our decision at $\alpha$ level of significant. But in two-tailed test , why do we give our decision at $2\alpha$ level of significant? Why do we not give the decision of ...
4
votes
1answer
58 views

Verifying independence for two Random Variables

Could you please give me some hints for the exercise below? Suppose we toss a coin once and let $p$ be the probability of heads. Let $X$ denote the number of heads and let $Y$ denote the number of ...
0
votes
1answer
15 views

confidence interval for a answer [closed]

In a survey of 48 citizens, 36 registered strong disapproval with their government's economic leadership. In the previous month, the proportion of participants registering strong disapproval was 65%. 
...
-4
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0answers
20 views

inference Single sample [closed]

Can someone Answer this question. Thanks in advance. 6.17 the one with black circle. Right now i have no idea how to approach and solve it.Any help would be highly appreciated. Thanks.
0
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1answer
40 views

What are the null and alternate hypotheses? Will you use a left, right, or two-tailed test?

Ben has a coin which he claims is weighted in a way so that when he flips it, heads appears more often than 50% of the time. He tries to prove it to you by flipping the coin 100 times, which ...
1
vote
1answer
26 views

How to evaluate a statistical test for fairness of a coin?

I suspect that a given coin is not fair, i.e that the probability of heads is not $\frac{1}{2}$. My question is not how we can prove the unfairness, but if we derive a test to check the fairness, How ...
2
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0answers
56 views

In confusion with a Bayesian statistical problem

I was learning some probability basics. I am stuck with a problem, that I need your help with in solving. An $e$-fair coin is a coin with probability of head $(\theta)$ in interval ...
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0answers
74 views

Basic problem in Bayesian inference

I have questions with the following Bayesian inference problem I found in the book by Bertsekas & Tsitsiklis (Introduction to Probability 2nd ed.). Problem is as follows (P.445, Problem 2): ...
3
votes
1answer
63 views

sum and product rules of probability

I am reading Bishop's Pattern Recognition and Machine Learning. In page 73, chapter 2.1. I can't understand the formula 2.19 : $$p(x=1|\mathcal{D})=\int_0^1 p(x=1|\mu)p(\mu|\mathcal{D})\text{d}\mu ...
-1
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0answers
27 views

Hyperplane data points

Would a single data point in the hyperplane (see below) correspond to a single cell in the data matrix or an entire row?
2
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1answer
64 views

Optimal Allocation

A campus population of size N=9000 is to be surveyed by a stratified sample for the prevalence of a certain disease based upon three strata of respective sizes $N_h$ = 1000, 3000, and 5000 for h = 1, ...
1
vote
2answers
95 views

Hat matrix,$H=X(X^{\prime}X )^{-1}X^{\prime}$

What is the importance of hat matrix, $H=X(X^{\prime}X )^{-1}X^{\prime}$ in regression analysis? Is it only for easier calculation ?
0
votes
1answer
38 views

Getting all zero correlations,$\rho_{ij}=\frac{\mathbb cov(e_i,e_j)}{(V(e_i)V(e_j))^{1/2}}$

Consider the general regression model $$Y=X\beta+\epsilon$$ where, $Y$ is an $(n\times 1)$ vector of observations, $X$ is an $(n\times p)$ matrix of known form, $\beta$ is a $(p\times 1)$ vector ...
1
vote
1answer
28 views

Uncertainty consistency?

The problem statement, all variables and given/known data I am given a set of x and y values x: (1,2,3,etc.) y: (1.2,2.2,3.1,etc.) with a given uncertainty and am asked a) find the best fit b) ...
0
votes
1answer
45 views

How to do multivariate regression in R?

I need to preform a multivariate normal regression in R. The question is: Let $Y_1$, $Y_2$, and $Y_3$ follows multivariate normal distribution. What is the conditional of $Y_3$ given ...
2
votes
1answer
53 views

Most efficient way to check answers to exercises when learning from a statistics textbook?

There's a community wiki at: Free statistical textbooks that has a nice list of freely available textbooks on statistics. Many of the textbooks that people suggest have exercises at the end of each ...
0
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1answer
17 views

Caculate Type II error for Binomial distribution

Basically this is a question if I got the general idea behind the Type II Error right. I’ll set up a little reproducible example: Given $p_0=0.6$ with an $\alpha$-level of $\alpha=0.1$. As Binomial ...
0
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0answers
24 views

Exponential distribution qq plot homework question

For an exponential qq plot, we fix the theoretical distribution to have λ=1. In order to compare the plotted points with the line y=x, what kind of rescaling should be applied to the data and why? ...
1
vote
1answer
26 views

Confidence Interval and Signifcance test Question

I have done the first part of the question already I just need help on the second part. You read in a U.S Census Bureau that a 99% confidence interval for the mean income in 2005 of American ...
1
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0answers
17 views

Statistics:Power Question Update [duplicate]

I have already asked this question but I did not initially give out all the details on the question, like the question being a multiple choice question. You manufacture and sell a iron rod whose ...
1
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1answer
106 views

Statistics: Power question

I have already answered this question I just like some feedback on am I right or wrong? You manufacture and sell a iron rod whose electrical conductivity is supposed to be 10.1. You plan to make ...
0
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0answers
27 views

Determining which t-test is right?

I have already solved this question, but I need some feedback. A new method for measuring blood pressure in laboratory mice using radiotelemetry has been proposed. How does this compare with the ...
4
votes
2answers
92 views

Distribution function of maximum of n iid standard uniform random variables where n is poisson distributed

I am studying probability theory on my own and am trying to work the following problem in the book - Let $X_1, X_2, . . .$ be independent, $U(0, 1)$-distributed random variables, and let $Nm \in ...
2
votes
1answer
110 views

Question with MLE

I'm having some problems with this question, and was hoping someone here could help. Let $X_1,\ldots,X_2$ be $n$ determinations of a physical constant $\theta$. Consider the model $X_i = ...
1
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1answer
105 views

What does it mean “being normally distributed”

There is an exercise which is used to illustrate how normal distribution works. The exercise starts by saying "Suppose scores on an IQ test are normally distributed..."; What does it mean for the ...
7
votes
1answer
147 views

What is the two-sample CDF of of $D^{+}$ and $D^{-}$ from the one-sided Kolmogorov-Smirnov Test?

I am trying to understand how to obtain $p$-values for the one-sided Kolmogorov-Smirnov test, and am struggling to find CDFs for $D^{+}_{n_{1},n_{2}}$ and $D^{-}_{n_{1},n_{2}}$ in the two-sample case. ...
2
votes
1answer
95 views

Plain english explanation of the Rayleigh distribution?

I need to understand the Rayleigh distribution for a homework assignment in computer networks. Unfortunately, I lack the background knowledge in the field of statistics and probability theory to ...