Questions tagged [self-study]

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

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21 views

Find the best linear unbiased estimate

I don't even know how to approach this problem ? Why are two different models given and how do I interpret the covariance matrix?
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18 views

Essence of matrix in linear regression model

b) I cannot understand the purpose of A matrix Also the purpose of X'e matrix in part f)
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21 views

F test on restricted linear regression

Is the following null hypothesis of ii) and iv) part correct: ii)B3+B4+B7=0 iv)B2 +B3=2(B5+B6) I am confused between combined and added effect of variables . In the iii) question number of ...
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2answers
63 views

Sum of a random number of r.v.'s [on hold]

A fair coin is flipped independently until the first Heads is observed. Let the random variable K be the number of tosses until the first Heads is observed plus 1. For example, if we see TTTHTH, ...
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25 views

UMVUE about Bernouli [on hold]

Find the umvue of θ when X1, X2, . . . , Xn are independent Bernoulli (θ) random variables. Check that your estimator does have mean θ^2 I am confused about how to get E(τ |T = t) = t(t-1)/n(n-1)
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17 views

Complete Sufficient Statistic of Uniform $(\theta,2\theta)$

Let $X_1,....,X_n$ be iid Uniform $(\theta,2\theta)$ , $\theta >0 $ It is easy to show that $T=(X_{(1)}, X_{(n)} )$ is a sufficient statistic for $\theta $ and we want to show it is not a complete ...
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1answer
17 views

Sufficient Statistic of Uniform $(-\theta,0)$

Let $X_1, ... , X_n$ be i.i.d random variables Uniform $(-\theta,0)$ , with $\theta > 0$ parameter \begin{align}f_{\theta}(x_1,x_2,\cdots,x_n)&=\prod_{i=1}^nf(x_i;\theta) \\&=\frac{1}{(\...
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6 views

Auto-Encoders with Sparsifying Non Linearity - sparsify function

I am currently studying for an exam and one topic are auto-encoders. The slides mention that one good encoding function could projecting the data and applying a sparsifying function, like so: $$r_i = ...
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19 views

Find the probability that number of items produced in a week is atleast 130

Number of Items produced in a factory during a week is a random variable with mean 100 and variance 400. What is the probability that this week's production is atleast 130? My attempt: using ...
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31 views

Number of samples to distinguish between artists and non-artists [closed]

I am not able to find the right formula to apply for this problem: A-Tier Artists $$P(success|art) \ge 0.5$$ B-Tier Artists $$P(success|art) = 0.25$$ $$P(art) = 0.5$$ What is the minimum number of ...
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26 views

Binomial Distribution variable classification

Situation: A coin has a probability for heads p=0.5 on any independent flip. After flipping the coin N=2,500 times, heads occurred G=53% of the flips. Question: The change in which parameter (only 1 ...
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28 views

Confused in the hypothesis testing problem

To test $H_0:\theta=\theta_0$ against $H_1:\theta \neq \theta_0$ when a sample $X_1,X_2,…,X_n$ is taken from $Rectangular(0,\theta)$. Now if we consider two cases $\theta_0< \theta_1$ and $\theta_0&...
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1answer
28 views

Doubt in neyman pearson lemma problem while considering the critical region

The given problem is X follows $Rectangular(\theta,\theta^2)$ To test $H_0:\theta=2$ against $H_1:\theta=3$ They asked to calculate the power and size if given crictical region is $X\geq4.5$ Now they ...
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17 views

Testing of hypothesis while range is depending on parameter [duplicate]

$f(x|\theta)$=$e^{-(x-\theta)}$,$x\geq\theta$ and 0 elsewhere Now we want to test $H_0$:$\theta\leq\theta_0$ against $H_1:\theta>\theta_0$ So here likelihood function is,$L(x|\theta)=e^{-\sum X_i+n\...
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5answers
262 views

How to interpret regression function with categorical variable?

I am trying to figure out how to interpret a regression function with no intercept and one categorical variable performed on a survey data. Each participant marks which actions, from a list of 25, ...
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29 views

What is the likelihood function of the starting time of diffusion?

I need to find the likelihood that a set of molecules was instantaneously released at time $t_0$, say $t_0=0$. Toy System Example: Let $N$ be the set of molecules released from a specific point in a ...
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11 views

Results of grid approximation and analytic determination of posterior probability

I am learning Bayes methods and cannot reconcile my grid approximation estimate of the posterior with an analytic solution. My prior has 5 events from 129 trials. My observed data has 13 events from ...
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2answers
90 views

If $X$ follows standard normal distribution, find the correlation coefficient between $X$ and $\Phi(X)$

If $X$ follows standard normal distribution, find the correlation coefficient between $X$ and $\Phi(X)$, where $\Phi(X)$ is the cdf of $X$. My attempt is: First we have to calculate $Cov(X, \Phi(X))$...
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1answer
75 views

Conditional Expectation (Poisson) UMVUE

Suppose $X_1,X_2,\ldots,X_n$ is a random sample from a Poisson distribution with mean $λ$. How can I find the conditional expectation $E \left( X_1\times X_2\times X_3 \mid \sum_{i=1}^n X_i= z \right)$...
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1answer
71 views

Why is bagging stable classifiers not a good idea?

Citing Bagging Predictors, Section 4 (emphasis mine): Let each $(y, \mathbf{x})$ case in $\mathcal{L}$ be independently drawn from the distribution $P$. Suppose $y$ is numerical and $\phi(\mathbf{x}...
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110 views

Understanding equation used by Hastie et al

I am trying to recreate FIGURE 3.6 from Elements of Statistical Learning. The only information about the figure is included in the caption. I am not clear on what the equation on the Y-axis means ...
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1answer
32 views

Self study of basic probability: Can't solve exercise

I am currently working through 'Concepts of probability theory by Pfeiffer' and can't solve the following problem: A carnival man hides a pea under one of three nut shells. By a series of complicated ...
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1answer
39 views

Please Check my solution and correct me (Testing of hyposthesis)

A sample of size 1 is taken from Poisson($\lambda$).To test $H_0:\lambda=1$ against $H_1:\lambda=2$,Consider a nonrandomised test $\phi(x)=1$ if $x>3$ and $0 \text{ for } x\leqslant3$.Find type I ...
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2answers
56 views

Probability density function with an unknown constant

I have a question that has a probability density function which is a function of two variables, x and y, and it also is defined in a unit square in the first quadrant. I assume its value is zero ...
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0answers
36 views

MCMC in Gibbs: Threshold Multivariate Linear Regression

I have a problem regarding what I expected to be a rather straightforward modelling approach: I want to investigate multivariate linear regression parameters and a thresholding parameter which defines ...
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1answer
31 views

How can I normalize Bayesian Network query result?

While taking a Bayesian network tutorial on YouTube, I was watching a video explaining the Bayesian Network probability inference. Somehow, at the end of the tutorial, the lecturer did not explain how ...
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0answers
21 views

Meaning of Degrees of freedom [duplicate]

We say chi square with $n$ degrees of freedom. It reduces if different constraints are introduced. What is the concept behind degrees of freedom?
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1answer
27 views

Is conditioning always increase the probability of some event

Is conditioning always increase the probability of some event ? My answer is, since by conditioning we are reducing the sample space probability must increase. Am I correct??? If not please explain me
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36 views

Please clear my doubt on this

Is it sufficent to show that $Var(S_n)/n^2$ do not converge to $0$ as $n$ tends to infinity in order to show that weak law of large numbers do not hold. Here $S_n$ is the Sum of the random variables ...
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23 views

Interpret interaction terms in Poisson

I'm using GLM to represent a Poisson model with the log link function. The response variable is a count variable representing the number of deaths. Both temperature and season are explanatory ...
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1answer
19 views

Odds of an event happening over a long period of time

If there is a fluctuating chance of rain throughout the day how do you calculate the chance that it will rain at some point throughout the day? For example, tomorrow there is a six hour period with ...
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1answer
51 views

EM algorithm and Mean residual life

I am reading Robert Hogg's (Introduction to Mathematical Statistics) EM algorithm. In example 6.6.1 (page 370 in the 7th version), please help to explain how the following integral $$\int_a^\infty(...
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1answer
31 views

Why CNNs are less prone to overfitting?

I'm doing a course on CNN by Andrew Ng. and in one of the lectures he said that due to Parameter Sharing and Sparsity of Connections in CNN it has fewer parameters which enables it to be trained with ...
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1answer
37 views

Hints needed in expectation calculation

I'm currently at a loss when calculating an expectation from a joint density function. This function is: $f_{XY}(x,y)=xe^{-10xy}(0.9)^{x-1} , y > 0, x \in \mathbb{N}^{+}$ and I'm required to do $E(...
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1answer
39 views

Does $E|X_n|^r\to E|X|^r$ imply $X_n$ converges to $X$ in $r$th mean?

If $X_n$ is a sequence of random variables and it converge to $X$ in $r$th mean then we say that $E|X_n-X|^r\to 0$ as $n$ is large. And it also implies that $E|X_n|^r$ goes to $E|X|^r$ for large $n$. ...
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40 views

Convergence in probability does not imply convergence in $r^{th}$ mean

I am confused regarding convergence in probability and convergence in $r^{th}$ mean. I am able to prove that convergence in $r^{th}$ mean implies convergence in probability, which is not true. Let me ...
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9 views

Converting a grid (or correlation matrix) to a single-axis table which summarizes the relationships

Say I have a correlation matrix/ grid (in Excel), similar to as follows: I'd like to convert this into a table whereby each interaction is captured, such as: I'm an R novice, but would like to ...
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1answer
63 views

Show that $nX_{(1)}$ is not consistent

Consider a random sample from exponential distribution with mean $\frac{1}{\theta}$. I have to prove that $nX_{(1)}$ is not consistent for $\frac{1}{\theta}$ . A sufficient condition for consistency ...
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1answer
44 views

A simple question from ANOVA

As per definition of $F$ statistic, $F= \frac{MST}{MSE}$ where MST and MSE denote mean square due to treatment and error respectively. From this definition of $F$ am I right in saying that $F$ ...
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0answers
18 views

Stationarity and invertibility conditions for ARMA(1, 1)

I am working on some homeworks and I have some troubles understanding one task regarding ARMA(1, 1) model and stationarity conditions: $y_t = Φy_{t-1} + ε_t + θε_{t-1}, ε_t ~ iidN(0, σ^2)$ What are ...
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0answers
36 views

Determining the limiting distribution of MLE

Let $X_i$ be i.i.d. with density $p(x) = ce^{-x^4/12}$, $c$ is a normalizing constant. Consider the location model $p(x-\theta)$. Aim is to compute the limiting distribution of the MLE. If I have ...
3
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2answers
68 views

UMVUE for probability of cutoff

Let $X_i \sim N(\mu,1)$, i.i.d. We aim to find UMVUE for $p(\mu) = P_{\mu}(X_1 \leq u)$ for some fixed $u$. I have shown that $\bar{X}$ and $X_1 - \bar{X}$ are independent. ($\bar{X}$: sample mean). ...
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1answer
47 views

ARIMA vs SARIMA

I am a self learner, and I am studying time series analysis. I came through the fact that ARIMA can be used to model a time series which is not stationary (Integrated ARMA model). The non ...
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45 views

Which statistical methods to be used?

I am analyzing data in order to show the reasonings of interindividual variabilities of the results of a laboratory data that was measured repeatedly over 100 hours in a single group. But the timings ...
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1answer
47 views

How to express a correlation matrix in terms of a covariance matrix?

I'd like to know, if I have the following Normal multivariate structure $$\left( {\begin{array}{*{20}{c}} {{Y_{r_1}}}\\ {{Y_{r_2}}} \end{array}} \right)\sim{\mathcal{N}_{r}}\left( {\left[ {\begin{...
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1answer
33 views

Stating a confidence interval for odd ratio

A research institute surveyed 1000 online shoppers in the United States and China. One question asked if the online shopper followed brands they purchased through social media. Here are the results <...
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45 views

Does the Markov property always hold for a state-space structure?

Markov Property: $p({\bf x}_t | {\bf x}_1, \ldots, {\bf x}_{t-1}) = p({\bf x}_t | {\bf x}_{t-1})$ Consider the following model for which the hidden states are ${\bf x}_t$ and the observations are ${\...
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1answer
24 views

Probability proportional to size

Consider the problem of drawing a sample of size $2$ from a finite population of size $20$ . The sampling is done with replacement using probability proportional to size scheme . The normed size ...
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0answers
39 views

BIBD MCQ PROBLEM

Consider a balanced incomplete block design ( i.e BIBD ) with parameters $(b,k,v,r,\lambda)$ , $b$ = number of blocks $\\$ , $\\ $ $k$ = number of plots $v$ = number of treatments $\\$ , $\\ $ $...