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11 views

Markov Chains, random valk

Show that the random walk has no stationary distribution. Give the distribution of $X^{(t)}$ for $t=10^4$ and $t=10^6$ when $x^{(0)}=0$, and deduce that $X^{(t)}$ has no limiting distribution ...
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0answers
22 views

Why does the normality of the coefficient's probability distribution follow from the normality of the errors in OLS?

So suppose after an OLS regression we want to know what the chance(P-value) is that the Beta coefficient is 0 . First we assume that many random processes caused the errors ($\epsilon\!_t$), meaning ...
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0answers
19 views

Is the MAP estimate always identical to the ML estimate when a diffuse prior is used?

Let's say I have two normally distributed variables: say height and body mass. I want to estimate the Pearson's correlation coefficient between them. I have a model that estimates the mean and SD of ...
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votes
1answer
48 views

Number of combinations with elements from different sets

Unfortunately I could neither find nor develop a closed formula, but I believe there is a simple solution for this problem. Could you please help me? Suppose that there are 4 different sets: Set A, ...
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0answers
16 views

Reference help MCMC

I am studying on Markov chains, random walks, gibs chains and optimizations using methods such as bisection and Newton Raphson, but am finding that the references that I have a little complex, like to ...
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1answer
26 views

Left-censoring , $Y_i=\text{max}(T_i,U_i)$

In the book , Statistical Models and Methods for Lifetime Data , in Left-censoring , it is written that Can only observe $Y_i=\text{max}(T_i,U_i)$ . Where , ...
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0answers
15 views

Colour Critical Graph Proof [migrated]

Let G = (V, E) be a simple graph. We call G colour-critical if χ(G) > χ(G\v) for all v ∈ V . Prove that if G is colour-critical with χ(G) = k, then d(v) ≥ k − 1 for all v ∈ V . Can someone please ...
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0answers
38 views

Imposing a model on a pdf

(This question is an attempt to zoom in on the key issue in this question using as little information as possible.) Lets say I want to derive the likelihood function of $\beta$ given $x$ and $y$ for ...
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3answers
66 views

Understanding Sampling with replacement

I am doing Stat110 and in the book, "Introduction to Probability" they give the following definition of sampling with replacement: Theorem 1.4.5 (Sampling with replacement). Consider n objects and ...
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0answers
37 views

Derivation of likelihood function for latent variable model made explicit

I am trying to make the steps deriving the likelihood function for the following latent variable model as explicit as possible: $$Y^0=X\beta + u$$ where $$u \sim NID(0,\sigma^2).$$ The observed data ...
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0answers
22 views

Mean,Median and Mode [on hold]

Responses to a survey question about eye color are coded as 1 (for brown), 2 (for blue), 3 (for green), 4 (for hazel), and 5 (for any other color). Does it make sense to find the mean, median, or ...
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0answers
10 views

Pivot properties (CB 9.10)

I am looking for help with Casella-Berger question 9.10. The question asks: Suppose that Q(t, $\theta$) is a monotone function of t for each value of $\theta$ in $\Theta$. Show that if the pdf of T, ...
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0answers
25 views

Basic Power test and Power test using ncp do not match

I am referencing 18.5 section of http://www.cyclismo.org/tutorial/R/cholesterol.html ,data is available to download and test. The case study asks to perform a ...
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0answers
25 views

Multinomial distribution pdf and fisher information matrix

The question is from Robert Hogg etal's Introduction to Mathematical Statistics 6th Edition Page 347 Example 6.4.5. It says: Consider a random trial which can result in one, and only one, of k ...
3
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1answer
25 views

Covariance of 2 sequences of random variables

We have a random number generator that generates random integers independently uniformly distributed from 1 to 5, inclusive. This random number generator is used to generate a sequence on $n$ ...
2
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0answers
15 views

How to test hypothesis on the composition of CAPM portfolios

I'm facing two different portfolios in CAPM framework derived as $$\hat{\omega}_P=\hat{\Sigma}^{-1}\frac{E(r)-r_f}{H}(\hat{\mu}-\iota'r_f)$$ on the same assets but, for example, on different time ...
0
votes
1answer
34 views

Proving the sum rule of probability limits

I'm trying to show that if $X_n$ converges in probability to 0 and $Y_n$ converges in probability to 0, then $X_n+Y_n$ converges in probability to $0$, ie the sum rule for probability limits. What ...
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0answers
13 views

Expression that better predicts the behavior [on hold]

I'm doing a self-study training of Statistics and I'm stuck with an exercise. If someone could help me... I'm using decathlon data of FactoMinerR plugin and I need to find the expression that better ...
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0answers
21 views

markov chain question [closed]

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. ...
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0answers
27 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 ...
0
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1answer
35 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 ...
0
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0answers
27 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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1answer
64 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
23 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 ...
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0answers
33 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
41 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
32 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, $E(theta)\frac 1 2 - (\theta)\frac 1 2 = 0$, ...
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1answer
51 views

Applying the T-test [closed]

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
43 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
27 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 ...
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0answers
36 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 ...
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1answer
218 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
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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
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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
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1answer
57 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
31 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 ...
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
73 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 ...
1
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1answer
42 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 ...
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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
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
29 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
19 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
74 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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0answers
33 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) ...