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2
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0answers
15 views

How to calculate probability of a random sampling of a population

Let's say that I have a city for which I know the size in square miles and I want to know the probability of a random sample of individuals from that population living within a certain threshold of ...
1
vote
1answer
23 views

Probability conjunction addition proof

I have been tasked with proving the following theorem. $$P(A) = P(A \wedge B) + P(A \wedge \neg B)$$ This is homework, so only hints are required (and would be greatly appreciated). I am well aware ...
0
votes
0answers
20 views

understanding E step of EM for GMM

I'm reading this chapter about EM (9.3.1) of the book "Pattern Recognition and Machine Learning". I understand the basic EM algorithm for GMM, but I'm having some problems understanding the ...
0
votes
0answers
12 views

Expectation of winning numbers on lottery ticket

A lottery consists of choosing 11 different numbered balls (the winning numbers) at random from a group of 100 numbers. A player chooses 11 numbers on a ticket. What's the expected number of winning ...
0
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0answers
12 views

Is there any point to Reverse Engineering the Fisher Information Matrix from an Inverse Covariance Matrix?

Would there be any advantage in deriving a Fisher Information Matrix backwards from an inverse covariance matrix? I've discovered that this is much easier to do on the SQL Server platform I use than ...
0
votes
1answer
21 views

Which to choose , Sample Mean or Population Mean [on hold]

If you are given some data say 14 models of camera used in 2014 and you are told to compute mean.Is that population or sample mean.
0
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0answers
12 views

Using Ito's Formula to find dX(t) on exponential functions

I have the following HW problem: Using Ito's formula, I have found dX(t) = B(t)$e^{tB(t)}$ dt + t $e^{tB(t)}$ dB + 1/2$t^2$ $e^{tB(t)}$ $dB^2$ However, I was wondering if I could find a ...
0
votes
0answers
19 views

Find mean of Poisson process between two known options

I think my question is simple, but somehow it's ruining my day. My problem is: I observe a Poisson process, and I want to find out which, between two known options, mean_1 or mean_2, is the true ...
0
votes
0answers
14 views

Difference of two Uniform Random Variables [duplicate]

Suppose $A \sim Unif(X, X+1)$ and $B \sim Unif(0,1)$. Find $P(A > B)$. ($A,B$ independent) I started out the following way: $P(A > B) = P(0 > B - A) = P(Z < 0) $, letting $Z = B - A$. ...
0
votes
0answers
24 views

General approach to learning a graphical model

Lately I've been reading a lot about inference and learning in probabilistic graphical models. I mostly understand specific methods (e.g. junction tree, message passing, MCMC; gradient descent, ...
1
vote
1answer
13 views

3 Stage Least Squares or 2 Stage Least Squares

I am planning on running a 3 equation simultaneous equation model where each of the dependent variables depend on each other (i.e. Y1 is based on Y2 and Y3; Y2 is based on Y1 and Y3; Y3 is based on Y1 ...
2
votes
1answer
54 views

Order Statistics, Expected Value of range, $E(X_{(n)}-X_{(1)})$

$X_1, X_2,...,X_n$ is a random sample from $U(0,\theta)$. Find $E(X_{(n)}-X_{(1)})$. I attempted this question by first finding the CDF of $X_{(n)}-X_{(1)}$ using the formula: $$F_{U}(u)= ...
1
vote
0answers
9 views

Is this simultaneous equation model identified?

I have a 3 equation simultaneous equation model where all 3 dependent variables depend on each other (i.e. Y1 is based on Y2 and Y3; Y2 is based on Y1 and Y3; Y3 is based on Y1 and Y2). Would all 3 ...
0
votes
0answers
6 views

Using the composition algorithm to generate a standard normal variate

This is regarding a question from a past exam that I came across but it has no solution. Given that I can generate random variates from the absolute value of a standard normal variate $X$, with pdf ...
1
vote
0answers
16 views

Variance-Covariance matrix of Weibull Distribution for right-censored data

The probability distribution function, cumulative distribution function and survival function of Weibull distribution are given by respectively, \begin{equation} f(t;\alpha, \beta)= ...
0
votes
0answers
7 views

One sample test or 2 sample test [on hold]

Pepsi is marketing, too see which one people like better coke or Pepsi. we know there are 19 people, and 11 choose Pepsi and 8 choose Coke Initial hypothesis is qp=.5 and alternative is 9 is not ...
0
votes
1answer
33 views

Multicollinearity - continuous and dummy variables

I know that one of the assumptions of Gauss-Markov is no perfect multicollinearity. If I want to run a model that estimates the effect of gambling on wages, would this model be appropriate: Wage = ...
2
votes
1answer
26 views

Fixed effects and time-invariant variables

I understand that fixed effects removes time-invariant variables, e.g. gender dummy, race dummies, etc. What will fixed effects do to variables that do not vary much over time? For example: Wage = ...
3
votes
2answers
69 views

Computing conditioned probability of $X$ by $U=\min(X,Y)$

Let $X$ and $Y$ be independent random variables with $P(X\leq x)=F_x(x)$ and $P(Y\leq y)=F_y(y)$. Let $U=\min(X,Y)$. I know that $F_u(u)=1-(1-F_x(u)(1-F_y(u))).$ By definition: $P(X \leq x |U=u)= ...
0
votes
0answers
31 views

Question about the normal distribution [on hold]

If you randomly sampled a population and obtained an observation equal to zero, would you believe that the population was normal with a mean of 2 and a variance of 2? What if you obtained 10 ...
0
votes
0answers
21 views

a question on time series [on hold]

I'm studying with time series. Please tell me whether there exist trend for each plot. I think that there exist. But I want to check it. ,thank you
0
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0answers
6 views

Why is a fractional factorial design $2^{9-5}$ of resolution 3?

I was sort of self-studying a poorly-elaborated lecture note of factorial design. It mentioned that a $2^{9-5}$ design has resolution 3. This is checked with the table below. It has $2^4=16$ runs, ...
0
votes
0answers
12 views

Joint PDF of ordered statistics [on hold]

Let $Y_1 < Y_2 < … < Y_n$ be the order statistics of $n$ independent observations from a continuous distribution with cumulative distribution function $F(x)$ and probability density ...
2
votes
1answer
36 views

How to deduct the coefficient of the Dirichlet distribution?

I am studying the textbook Introduction to Probability Models by Sheldon Ross. In Section 3.6 page 151 (10th edition), the author uses the Dirichlet distribution to deduct the coefficient of a ...
0
votes
1answer
34 views

Does the following pmf belong to the exponential family?

I recently saw* a pmf: $f(y)=\frac{\mu^y}{(y!)^\theta z(\mu,\theta)}$, where $z(\mu,\theta) = \sum_{i=0}^{\infty}\frac{\mu^i}{(i!)^\theta}$. * It is a bonus question on a homework assignment. My ...
0
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0answers
6 views

Given Pivotal Quantities Find Confidence Limits

Based on the pivotal quantities below $Q_{1} = \frac{ \hat{\theta_{1}} - \theta_{1}}{ \hat{\theta_{2}}} , Q_{2} = \begin{pmatrix} \frac{\hat{\theta_{2}}}{\theta_{2}}\end{pmatrix}^{-1}$ ...
-1
votes
1answer
35 views

Sample mean and sample variance [on hold]

The sample mean is $\bar X = \frac{1}{n}\sum_{i=1}^n X_i$ and the sample variance is $S^2 = \frac{1}{n-1} \sum_{i=1}^n (X_i - \bar X)^2$ Can someone please explain how the sample mean and sample ...
1
vote
0answers
6 views

ANOVAS and Planned Comparisons

I'm fairly new to stats and we have been asked to conduct our own one way ANOVA's for class. Our first hypothesis is that gender will effect exercise. Our second is more one tailed, Men will ...
1
vote
0answers
30 views

Can an independent t-test be used on paired data when the pairing is unknown?

Suppose the effectiveness of a training course is examined, and performance of each individual in a group is taken both before and after, and the differences are compared in a paired $t$-test. Would ...
0
votes
0answers
31 views

Expectation Maximization (EM) for 3-dimensional parameter $(\alpha,\mu_2,{\sigma}^2)$

Let $x_i$ where $i=1,...,100$ are iid observations from a mix of two normal distributions with means $\mu_1=0$ and $\mu_2$ and the same variance ${\sigma}^2$. If $\alpha$ is the proportion of the ...
-1
votes
0answers
25 views

Finding the distribution and covariance matrix of a distribution

Question: Let X and Y be two continuous random variables with joint probability density function $$f(x,y)=\begin{cases}\frac{1}{2} & \text{if} \ \lvert x \rvert + \lvert y \rvert \le 1 & \\ 0 ...
1
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0answers
20 views

Showing independence between two functions of a set of random variables

I've been working on the following problem and I'm confused about how to get started: Let $X_1, X_2,..., X_n$ denote $i$.i.d. real valued random variables, each absolutely continuous with an ...
1
vote
1answer
38 views

Exercise given a sequence of i.i.d. real RV and a distribution function $F$ need to verify three statements for $Z_n=n \min (X_1, \dots , X_n)$

Pardon the title, I couldn't think of a better one. The three statements below are to prepare for a tougher exercise (which I could solve) however I am lost on 1 of the statements. Problem: Let ...
-1
votes
0answers
35 views

How do I calculate for mean and stadard deviation when given only %

The weight of a newly born baby at a particular hospital is normally distributed with mean μ and standard deviation σ. 5% of the babies weighed more than 5.1kg and 10% of the babies weighted more ...
0
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0answers
18 views

Estimate polynomial model [on hold]

For a polynomial regression of temperature data I want to estimate a polynomial model of order 8. It is asked for a suitable prior that mitigates the problem of 1) overfitting the data 2) higher ...
0
votes
0answers
18 views

ARMA to Pure AR or MA [closed]

Hello, Given that an ARMA(P,Q) process can be written as an MA or AR infinite process, I am confused as to how this would work for the attached example where P=Q=1?
0
votes
0answers
13 views

Fill in the blank [closed]

Given that the mean dollar amount spent on groceries by a couple per week is $\$150$ with a standard deviation of $\$12$, at least ___% spend between $\$126$ and $\$174$ per week on groceries. Do not ...
1
vote
0answers
25 views

Is Sea Level Rise Data from NOAA an Areal Data?

I am working on sea level rise and I collected the data from NOAA. In the meta, they describe the data is obtained by : Hourly : three-point Hanning filter ...
0
votes
1answer
29 views

Questions on Examples of Introduction to Probability Models

Here is the question: Suppose there are 25 different types of coupons and suppose that each time one obtains a coupon, it is equally likely to be any one of the 25 types. Compute the expected number ...
1
vote
2answers
57 views

Point null hypothesis in Bayesian statistics

Let $X\sim N(\theta,1)$ and consider 5 independent observations $X=(4.9,5.6,5.1,4.6,3.6)$. The prior probability that $\theta=4.01$ is $0.5$. The remain values of $\theta$ are given a prior ...
0
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0answers
40 views

What statistical test should I use for this question?

You discover an isolated tribe living in a forest. Each member of this tribe has an unusual bacterium in their colon. You take a sample of bacterial cells from 6 random villagers and measure the ...
1
vote
0answers
29 views

Bayesian linear regression - Defining hyperparameters

I am currently working on a linear regression task from a textbook and I have some questions. In the following you will find the task as well as some thoughts of mine to possible results. Short ...
0
votes
0answers
21 views

Determining the required sample size to meet a bound

A company produces a special kind of utility terminals. It has N = 26016 such terminals out in the field in some city for many years. Over time these utility terminals go bad. The company decides to ...
1
vote
1answer
19 views

Reference to Statistical Control Quality

This semester I'm taking a Green Belt course. I'm really enjoying it and I want to go more deeper in that, I already take this book to start to study Introduction to Statistical Quality Control does ...
0
votes
1answer
16 views

The square of each t-statistics is the corresponding F-statistics

The below text is from statistical learning Page 76-77. The data used in the following example can be found here . I just want to know how to calculate $RSS_0$ (It is different from TSS) As ...
0
votes
0answers
31 views

Improving multiple regression model

I can't upload the graph due to my low reputation. However, if you want me to email you that I can email it to you. 1) Is there a problem with this model? I need ways to improve the base model. ...
3
votes
0answers
55 views

Why Type III ANOVA is used for this analysis of coefficients

Note that I'm giving (what I believe) is minimal information to solve this problem. If more details than what are provided here are needed, please let me know, and I can provide them. I have a model ...
0
votes
0answers
8 views

Explanation on time complexity for nearest neighbor search

My problem is related to the approximate nearest neighbor search. I found a useful link ...
0
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0answers
39 views

bio statistic question in epidemiology [closed]

A cancer screening test is being applied in a population of 200 men who were also evaluated through the biopsy of tumor. 30 of the men were confirmed having cancer through biopsy. Out of these 30, 25 ...
5
votes
0answers
52 views

Exercise on Borel Cantelli Lemma ($\lim \sup X_n/ \ln(n) =1$ a.s.) help required to rigorously write the statement

I hope this question is within the scope of this site. Please note that I have solved this Exercise, I do have doubts about my presentation though and about how to rigorously empathize on the ...