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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19 views

markov chain question [on hold]

There are two points which are A and B. The distance between A and B is 50meter. One person goes to A with probability 1/6, he goes to B with probability 3/6. And he goes nowhere with probability 2/6. ...
1
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0answers
25 views

Classifying groups using statistical significance

I am really struggling to get my head around some sample questions of my quant class. The exam is looming and I cant grasp what must be a basic concept. Sample A service provider has identified ...
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1answer
30 views

markov chain - probability question

Transition matrix has been written like that; $$\mathcal P = \begin{bmatrix} 1/3 & 0 & 2/3 \\ 1/3 & 1/3 & 1/3 \\ 0 & 0 & 1 \end{bmatrix}$$ the initial vector is that ...
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0answers
25 views

T-test formula when population standard deviation is known [duplicate]

I got this question from my mentor. Marks obtained by 10 MBA students in Statistics paper (out of 50) is given below. 20.5, 18.25, 10.23, 15.47, 35.62, 47.64, 12.30, 29.65, 38.5, 14.79. Test whether ...
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votes
1answer
58 views

How do I find $P(X + Y < 1)$?

$X$ and $Y$ are jointly continuous random variables, with $f(x, y) = 1$, then what is $P(X + Y < 1)$? Our teacher said it's $$\int_{0}^{1/2} \int_x^{1-x}1 \cdot dy dx.$$ I'm confused about the ...
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0answers
20 views

Using Boole's Inequality to Prove Observation

I'm walking through the book "Probability" by Jim Pitman book solo and cannot wrap my head around this problem; Use Boole's Inequality and the fact that, to prove. How do you approach this ...
-3
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0answers
30 views

If the null hypothesis is true, how will the test statistic be distributed?

I went with T~(50-6) The question goes.... "A regression is estimated with 50 observations, five explanatory variables and with a constant. Suppose You want to test the following hypothesis $H0: ...
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0answers
32 views

Linear regression - Simulation - “what if” scenario

I have an assignment at university and I have been given a simple situation which I would like to explain here. Situation: I would like to perform simulation on purchase price of a product and see ...
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0answers
29 views

Estimator, unbiased or biased

I am having difficulty with this. My procedure for solving it is that $$ E(\theta)= \frac 1 2 E(X-0.1) + \frac 1 2 E(X+0.1) = \frac 1 2 $$ So, $E(theta)\frac 1 2 - (\theta)\frac 1 2 = 0$, ...
-1
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1answer
51 views

Applying the T-test [on hold]

So far I have calculated the sample means $\overline{A} = 0.75$ and $\overline{B} = 2.33$. Using these I computed the sample variances: $S_A^2 \approx \frac{28.805}{9} = 3.2005$ and $S_B^2 = ...
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0answers
40 views

how can I tell whether the estimator is biased or not

$X_i\sim N(\mu,\sigma^2)$. Two independent samples of size $n_1$ and $n_2$, with means $\bar{X}_1$ and $\bar{X}_2$. Two estimators of $\mu$ are proposed: $\hat{\mu}_a = ...
1
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0answers
32 views

Weighted probability distribution function [duplicate]

I have found that if X has a weighted pdf then $E(X)$ is just the weighted $E(X_i)$'s and the same holds for the second moments. Can I cleanly express Var(X)?
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2answers
26 views

Expected Value Normal Distribution over an interval

The mean of a normal distribution is theta and variance is 1. I know that E(X)=theta. Then, if I compute the integral I would use to find E(X) but instead I only take the integral from (-a,a). How ...
1
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0answers
33 views

Rao-Blackwell exponential distribution

Let $X_1,..,X_n$ random sample of $X\sim\text{Exp}(\lambda)$ with $f(x;\lambda)=\frac{1}{\lambda}e^{-\frac{1}{\lambda}x}I_{[0,\infty]}(x)$ i) Find a unbiased estimator of $\lambda$ based ...
4
votes
1answer
214 views

Is the following dataset possible?

"Is it possible to create a data set where $\bar{x}=30.0$, range $R=10$ (meaning the max-min=10), and variance $s^2=40.0$?" I feel sort of dumb asking this question, but I'm not quite sure I'm on the ...
2
votes
1answer
30 views

UMVUE for a function

Let $X_1,...,X_n$ random sample $X$~$Bernoulli(p)$. For $n\geq 4$ show that the product $X_1X_2X_3X_4$ is a unbiased estimator for $p^4$, and use this fact for find the best unbiased estimator of ...
3
votes
1answer
62 views

Is it possible for an expected value not to exist?

A probability density family for $x\in\mathbb{R}$ is $$f(x) = k(\theta)\left[1 + (x/\theta)^2\right]^{-1}$$ parameterized by $\theta \gt 0$. I am supposed to find $k(\theta)$ and then both $E(X)$ ...
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0answers
12 views

Boosting in linear regression

Incremental Forward Stagewise Algorithm is a type of boosting algorithm for the linear regression problem. I would like to know what 'boosting' means. Does it keep on updating the coefficient of the ...
2
votes
1answer
55 views

Prove that limsup of a sum of iid random variables(with 0 expectation) is infinity

Let $Y_1, Y_2, Y_3,\ldots,Y_n,\ldots$ be iid and bounded random variables with $E[Y_1]=0$. Define $X_n = Y_1+Y_2+ \cdots + Y_n$. If $\Pr(Y_1 \neq 0) \gt 0$, then $ \limsup X_n = \infty$ with ...
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0answers
25 views

Find nonnegative X(t), Uniform Integrability (UI), sup X(t)<∞ a.s. but E sup X(t)=∞ [closed]

Find nonnegative X(t), Uniform Integrability (UI), sup X(t)<∞ a.s. but E sup X(t)=∞ How can I do??
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0answers
29 views

Confidence interval, lower and upper bound

I am studying on confidence intervals, but I'm still with some doubts Let a random sample $X_1,..,X_n$ with density $f(x;\theta)=\theta e^{-\theta x}I_{[0,\infty]}(x)$. Find a confidence interval for ...
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0answers
14 views

Reflection principle question [closed]

Question: $$P(X_1\gt 0, ..., X_n\gt 0, X_n=a-b)=?$$ Its Answer: $= (1,1) \rightarrow (n,a-b) $ that meet neither touch nor cross paths. $=[(1,1) \rightarrow (n,a-b) \ \ \text{all ...
2
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1answer
34 views

Clarify probability solution re. birthdays

I have a problem regarding birthdays that involve the possible birthdays a group of 5 people can have within the 7 days of the week. My solution to this was 5^7 total possibilities, but I'm not sure ...
2
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0answers
71 views

Confidence interval and probability

Suppose that $T_1$ is $100\gamma$ percent lower confidence limit for $\tau(\theta)$ and $T_2$ is $100\gamma$ percent uper confidence limit for $\tau(\theta)$. Further assume that ...
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1answer
41 views

Lower bound on the mean for an exponential distribution at a confidence level of 95%

for the life of me I simply cannot wrap my head around confidence intervals and upper/lower bounds on parameters. E.g $$ f(t;\tau) = \frac{1}{\tau} e^{-t/\tau}, \qquad t \geq0 $$ If $t=1$ (a single ...
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0answers
10 views

how to write these two inequality? (Asymptotic properties of m estimator)

$T_n^*:=sup\{t|\sum ψ(x_i;t)\gt 0\}$ $T_n^{**}:=inf\{t|\sum ψ(x_i;t)\lt 0\}$ As it's seen in the above figure, $-\infty \lt T_n^{*} \le T_n^{**} \lt +\infty$ Then, how to show that the followings ...
1
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1answer
27 views

Confidence Interval, uniform distribution

Let $X_1,...X_n$ random sample from $f(x;\theta)=I_{[\theta-\frac{1}{2};\theta+\frac{1}{2}]}(x)$. i) Show that $(X_{(1)},X_{(n)})$ is a confidence interval for $\theta$.ii) find your ...
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0answers
430 views

please clarify the solution? [closed]

I'm studying Problem5.3 and its solution. However, its solution is not clear for me. Please explanatorily show this answer . I need to learn such type of questions. Please help me. Thank you.
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0answers
19 views

Using statistical tables

How do I find from the table the range at which p value lie us the F-test when both the numerator and denominators are given say (6 and 18 respectively) and p-value of 4.25? what about using the ...
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1answer
28 views

UMVUE explanations

Let $X_1,...,X_n$ a random sample where $X$~Poisson$(\theta)$. i)Find UMVUE for $\theta$ ii)Exists UMVUE for $\frac{1}{\theta}$ For i) I found that $T=\overline{X}$ is UMVUE for ...
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0answers
16 views

UMVUE for pareto distribution

Let $X_1,..X_n$ random sample with $f(x;\theta,a)=\frac{\theta}{a}(\frac{a}{x})^{(\theta+1)}I_{(a,\infty)}(x),a>0,\theta>0$. Find the UMVUE for $\theta$ when $a$ is fixed. My attempt ...
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0answers
72 views

Inferring the lambda of a Poisson distribution

Lets consider the following scenario: We have 4 roads each with equal distance of 800 m. In traffic engineering, the ...
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32 views

What is Frequentist Inference?

Frequentist Inference is defined as (according to the tag wiki) : In the frequentist approach to inference , statistical procedures are assessed by their performance over a hypothetical long run ...
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1answer
36 views

Solving: Poisson Distribution query [closed]

The distribution of a number of printing mistakes per page per book is Poisson with mean 3. Given that $e^{-3} = 0.047987$, the probability that there is some mistake is a) 0.049787 b) 0.950212 c) ...
2
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1answer
32 views

Cramer-Rao Lower Bound

Let $X_1,..,X_n$ be an iid sample of $N(0,\sigma^2)$. Find an unbiased estimator of $\sigma^2$ and its lower bound. I found that $$\hat{\sigma}^2 = \sum_{i=1}^{n} X_i^2$$ is an unbiased ...
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0answers
24 views

explain the interpretation of the following proposition and how to prove it?

Please explain the interpretation of the following proposition and how to prove it? Proposition: Assume that $\exists t_0 $ s.t. $\lambda(t)\gt 0 $ for $t \lt t_0$ and s.t. $\lambda(t)\lt 0 $ ...
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0answers
33 views

How to calculate the randomness of a sample and if it is representative on r?

I am doing a project on R commander and the project says, "The set of exoplanets discovered to this day is a sample of all exoplanets that exist in the universe. Discuss whether you think this sample ...
2
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0answers
51 views

Show that MLE of $\lambda = \frac{n-T_n}{S_n+cT_n}$

$X_i$ are i.i.d exponential, mean $\lambda^{-1}$ for $1 \leq i \leq n$ and, the values are measured such that $X_i = c$ if $X_i \geq c$ and $X_i$ otherwise. Show that MLE of $\lambda = ...
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0answers
13 views

Proving that a distribution is a member of a monotone likelihood ratio family

I have a quick question about establishing something is MLR. Basically I don't see a statistic that this ratio clearly depends on. I have thought of some tricks but I am not quite sure if they work. ...
0
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1answer
26 views

estimates for least squares vs estimates for ridge

The coefficient estimates for RSS is given $\hat{\beta} = (\mathbf{X}^T\mathbf{X})^{-1}\mathbf{X}^T\mathbf{Y}$, while for ridge regression, $\hat{\beta}^\text{ridge} = (\mathbf{X}^T\mathbf{X} + ...
2
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2answers
94 views

Poker and the Birthday Problem

The number of possible poker hands drawn from a standard 5-card deck is ${52 \choose 5}$. This is sampling without replacement where order does not matter, e.g., ...
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1answer
32 views

Sparsity in Lasso and advantage over ridge (Statistical Learning) [duplicate]

I'm learning about the Statistical learning and in the section comparing Lasso and Ridge Regression it shows that the main difference between these two problems is the way the constraint/penalty is ...
4
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2answers
129 views

Convergence of a product of random variables

Let $X_1, X_2, \dots $ be a sequence of I.I.D. random variables with pdf $f(x) = \frac{8x}{9}, 0 < x < 1.5$. What does the product $\prod_1^nX_i$ converge to in the almost sure sense? Shouldn't ...
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1answer
80 views

Understanding the mean and rate of an exponential distribution

Background: In the field of Civil Traffic Engineering the arrival of the vehicles in a road is random process modelled by exponential distribution [1]. Illustrative example: Along this line, let's ...
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0answers
32 views

Logistic/Logit Regression Practice Exam Question

So I have an exam practice question which runs as follows: The logistic function of a number $x$ defined as $f(x)=\frac{1}{1+e^{-x}}$ Use this definition to write down the expected value of response ...
4
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1answer
49 views

SLLN applies to last $r_n$ variables?

Let $X_n$ be a sequence of IID random variables with finite mean and first moment, let $S_n = \sum_1^n X_n $ then is it true that \begin{equation} \frac{S_n - S_{n-r_n}}{r_n} \end{equation} ...
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0answers
25 views

customer analysis - book / blog recommendation?

I'm new to the topic 'customer analysis' (in general) and need advice for a good starting point: What is a good book / blog / tutorial on this topic? My current situation is: I have a lot of customer ...
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1answer
46 views

Seeking assistance with model formulation in a simple problem

I'm attempting to devise a mechanism by which gifts or rewards are distributed to players based their location (an area is divided into regions and I can compute if a player is within a region). I ...
3
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2answers
57 views

Bernoulli maximum likelihood

Suppose $X_1, X_2, \dots, X_n$ are iid Bernoulli(p) random variables. How do you find the restricted maximum likelihood for p where $0<p<0.5$? My work so far: Write out the likelihood: ...
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0answers
32 views

Estimation with ML or Bayesian

A marketing department is supposed to find the market share of their product. To answer this question, a survey among 720 representative people is conducted, 696 of which complete the poll with ...