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0
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0answers
9 views

Relation between two critical regions when the level of the test is changed

Based on a random sample of size n,denote the $\alpha$-level critical region for a hypothesis testing problem $H_0$ vs. $H_1$ as $C_{\alpha}$,if we change the level to $\alpha_1<\alpha$,then can it ...
0
votes
0answers
20 views

how can i calculate $E(Y)$ [on hold]

suppose $X$ is random variable non negative with Distribution function $F_{X}(x)$ and $Y$ is random variable with Distribution function $G_{Y}(t)=1-E(e^{-tX}) ,0\leq t$ . how can i calculate $E(Y)$
3
votes
1answer
30 views

Expected value of difference of two order statistics

$X_1,X_2,..,X_n$ is a random sample from the random variable whose pdf is, \begin{align*} f(x)=\lambda e^{-\lambda(x-\mu)},\mu<x<\infty \end{align*} How can we find $E(X_{(2)}-X_{(1)})$, if ...
0
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0answers
49 views

Impossible to bring to normality

I have given a data and I have to check the data if it's normally distributed and if not I have to transform the data into normality. I had done shapiro-wilk normality test and p-value is clearly ...
1
vote
0answers
17 views

Computing the number of renewals

My question is from the book Introduction to Probability Models, 10th edition, by Sheldon Ross. Page 463, $\S$7.8. There is a paragraph in the book talking about the computation of renewal function: ...
1
vote
1answer
19 views

Finding unbiased estimator of function of p from a geometric distribution

Let $X_1$ and $X_2$ be a random sample from the geometric distribution with $Pr(X_i=j)=p(1-p)^{j-1}$ for $i = 1, 2$, $j = 1, 2, \ldots$ and $0<p<1$. Which statistics $T(X)$ could be an unbiased ...
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0answers
36 views

Principal Component Analysis to Regression [on hold]

I am a student at one of the famous engineering schools but I have signed up for a Psychology class project which is due by end of June. Here is my peculiar situation. I was asked by my professor ...
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0answers
3 views

What is the difference between coverage probability and confidence coefficient?

Casella-Berger provides the following two definitions for an interval estimator [L (X), U(X)] of a parameter $\theta $ :- Coverage Probability: probability that the random interval [L (X), U(X)] ...
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0answers
11 views

Whole life cost question [on hold]

Hi I have a problem with this question "Consider the following costs for a new bridge with a projected service life of 120 years: Construction cost: 10 units Programmed maintenance: 1 cost unit ...
0
votes
1answer
21 views

Probability distribution arising from the combination of a normal variable and an other random variable

Let $X\backsim N(0,5^2)$ and Y be an independent random variable taking the values +1 and -1 with equal probability.Find the distribution of $S=XY+\frac{X}{Y}, T=XY-\frac{X}{Y}$ I have solved the ...
3
votes
1answer
64 views

Maximum of a set of values from given mean and median

The arithmetic mean and median of $5$ distinct natural numbers are both $7$,what may be the maximum of the $5$ numbers? Here we see that the median is the $3rd$ value.Also the sum of the numbers is ...
1
vote
1answer
34 views

Which of the followings can be regarded as sufficient statistics?

The probability of heads showing up upon tossing a certain coin is $p$, this coin is tossed $3$ times, let $X_i,i=1,2,3$ be $1$ or $-1$ depending on the outcome of the $i^{th}$ toss being head or ...
0
votes
0answers
17 views

Unbiased estimate of a geometric random variable

A coin for which the probability of heads showing up on tossing it is $p$ is tossed $15$ times.The first head appeared in the 3rd toss and 6 heads showed up in $15$ tosses,what are the unbiased ...
1
vote
1answer
75 views

Logistic Regression Problem

The following table gives data on income in thousand dollars (x), the number of families (N) at income x and the number of families owning a house (n). ...
0
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0answers
10 views

What does “complete i” subscript mean in Gelman's model of incumbency in congressional elections?

I'm having a look at section 14.3, "Regression for causal inference: incumbency in congressional elections" in Gelman et al's Bayesian Data Analysis, third edition, pages 358-362. I'm looking for the ...
2
votes
1answer
30 views

Sequence of probabilities

The probability distribution of a random variable X is $P(X=k)=p_k,k=0,1,2,...$ and $\frac{p_k}{p_{k-1}}=a+\frac{b}{k}$. If $p_0=\frac{1}{9},p_1=p_2=\frac{4}{27}$,what can be said about the sequence ...
5
votes
2answers
147 views

Unbiased estimator of poisson parameter

The number of accidents per day is a Poisson random variable with parameter $\lambda$, on 10 randomly chosen days the number of accidents were observed as 1,0,1,1,2,0,2,0,0,1, what will be an unbiased ...
2
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0answers
67 views

Unbiased estimator of binomial parameter

Let 4,3,5,2,6 are 5 observations of the binomial(10,p) random variable.What will be an unbiased estimate of $(1+p)^{10}$ ? I have tried to solve the problem in this way. We know that ...
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0answers
8 views

Why are these two samples correlated with each other (ISRL passage)?

On pg. 44 of Introduction to Statistical Learning: Here we create two correlated sets of numbers, x and y, and use the ...
0
votes
1answer
31 views

Computing Conditional Probability - $P(A|B^c)$

I'm terribly out of practice in even the most basic rules of probability, any help with the following question is appreciated. Essentially, I am having an issue with the application of the conditional ...
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0answers
19 views

Method assignment

I have a task in a method assignment. Its about correlation and significance. In a) Im presented with r= -0.37, p = 0.05 and my sample size is 30. b) A colleague says that the correlation wouldnt be ...
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0answers
5 views

Computing range of threshold values for given inputs and classifications

I'm having some trouble with the following type of exercises: Given a feed forward neural network with Heaviside activation function (the function that outputs 1 if the input is >= some threshold ...
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2answers
23 views

Pemutations and combinations problem

I have this one question in statistics: There are five women and six men in a group. From this group a committee of 4 is to be chosen. In how many ways can the committee be formed if the committee is ...
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0answers
7 views

Understanding minimum loss projection

I am trying to understand the paper: pseudo-metric online learning algorithm(Link). It intends to learn a matrix threshold pair by projecting it into space $C_t$ $C_t = ${$(A,b) \in R^{n^2 +1} : ...
3
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0answers
60 views

What statistical method to use? Heat treatment of bacterial spores

Here is my experimental design; I have four different strains of a bacterial spores. I am taking a fixed volume of spore suspension of these strains and subjecting them to heat treatment at the same ...
1
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1answer
34 views

What is the state-of-the-art non-parametric PDF estimation?

Below is some data points that are generated by a process that is normally distributed with $\mu=5$ and $\sigma=0.5$. But of course, we will pretend that we don't know the true distribution of the ...
3
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1answer
35 views

How to prove that $Cov(\hat{\beta},\bar{Y}) = 0 $ using given covarience properties

To quote: It is well known that, if $W_1, ..., W_n, Z_1, ..., Z_m$ are random variables and $a_1, ..., a_n, b_1, ..., b_m$ are constants, then $Cov ( \sum_{i=1}^n a_iW_i, \sum_{j=1}^m b_jZ_j) = ...
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0answers
11 views

Which is the PACF of an AR(2)

Which is the PACF(1) of the following AR(2) process? $$ y_t = \phi y_{t-2}+\epsilon_t $$ with $$\epsilon_t$$ a white noise with mean 0 and variance $$\sigma^2$$
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1answer
97 views

how can i calculate $E\left(\Pi_{i=1}^{n}\displaystyle\frac{X_i}{X_{(n)}}\right)$

suppose $X_1,X_2,...,X_n$ be a random sample of $U(0,\theta)$. how can I calculate $E\left(\Pi_{i=1}^{n}\displaystyle\frac{X_i}{X_{(n)}}\right)$. $X_{(n)}$ = $max_{1\leq i \leq n}X_i$
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0answers
15 views

Aggregate with custom function [closed]

I am new to statistics, I have quick doubt regarding the aggregate custom functions. Could you say what would be the sum(x) and length(x) for each row from the second snap? but am able to understand ...
0
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1answer
26 views

Is K-Means used the right way?

I have this model where I have a count of a word. Every day I do a count of the word and then calculate a simple ratio for this word by saying: ...
1
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1answer
20 views

choosing between traditional statistical models and neural networks using RMSE

I am new to neural networks, and am more familiar with classical linear regression type models. I have a basic question about choosing between the two in attempting to develop a predictive model. Is ...
3
votes
1answer
47 views

Correlation of order statistics from Uniform parent

Can someone please help me out with this sum? It says: If $(X_1, X_2, \dots, X_n)$ are a random sample from Uniform(0,1) distribution, find the correlation between the order statistics $X$ ...
0
votes
1answer
31 views

the graph of log(-log) for Cox model on survival analysis

I'm studying Cox Regression model on Survival Analysis. While testing validity of Proportional Hazard model, I will use log(-log) graph method in SPSS. First of all, I mention which procedure I'm ...
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2answers
55 views

What's the problem with my sports streaks problem solution?

The problem is from the book "Think stats". It's formulated as follows: If there are 10 players in a basketball game and each one takes 15 shots during the course of the game, and each shot has ...
3
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1answer
40 views

Proving a property of $(n-1)s^2$

I would appreciate your help as I climb the stats learning curve! I want to prove the following: "Let $x_1, x_2, ... , x_n$ be any numbers and let $\overline x = (x_1 + x_2 + ... + x_n)/n$ Then ...
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0answers
7 views

select the variables in the eqation binary logistic in spss [closed]

I have run binary logistic spss in order to check the significance in 9 categorical predictors in my master theses. When comes to output in the box of variables in the equation i dont know to what to ...
0
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0answers
60 views

seeking proof of a necessary condition of a beta inequality

Assume we have two Bernoulli trials with success probability $c_1$ and $c_2$ ($c_1>c_2$ and $c_1,c_2\in(0,1)$), respectively. Now we use two beta distributed random variables $e_1\sim ...
10
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0answers
1k views

Why is a square root not a linear transformation? [migrated]

The question says: Prove that the function $f(x)=\sqrt{x}$ is not a linear transformation (particularly $\sqrt{1+x^2}≠1+x$) I think that this is because the exponent of $\sqrt{x}$ is $1/2$, ...
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0answers
58 views

Standard error explanation [closed]

In which direction and how far away, in terms of standard errors, is the estimated  difference ( Diff x ) in Case 1 from the hypothesised value. So what I've done is calculated t0= estimate - ...
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0answers
5 views

Question regarding distributions and prediction

During my learning about distributions I came up with the following prediction algorithm. Given a dataset, for example a plot of stock prices to time. Select a range of values from the graph (for ...
0
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0answers
6 views

Question on how to setup the variables and study

Background: I work in a health care company that use phone calls to remind members for their insurance renewal. I want to find out what is the relationship of (number of phone calls vs. outcome), ...
1
vote
3answers
119 views

What is the distribution of $X_i-\bar{X}$ when $X_i$ has $N(\mu,\sigma)$ distribution

Suppose $X_1,X_2,...,X_n$ be iid random variables with $N(\mu,\sigma^2)$ distribution. We know that $X_i-\mu$ has a $N(0,\sigma^2)$ distribution. My question is what is the distribution for ...
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0answers
15 views

Why when minimizing the forward Kullback-Leibler Divergence w.r.t a factored approximation is it correct to set Q to be the product of marginals?

The following question is from Mackay's 2004 textbook. Consider the problem of approximating a joint distribution $P(x, y)$ by a separable distribution $Q(x, y) = Q_X(x)Q_Y(y)$. Show that if the ...
2
votes
1answer
66 views

R: default correlation in nlme::lme

I just noticed that the default correlation of nlme::lme() is NULL. The explanation of argument for correlation is correlation: ... Defaults to NULL, corresponding to no within-group ...
3
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0answers
78 views

what is this property? $\int p(x,\pi)d\pi=p(x|E[\pi])$?

Sorry if the title does not make sense, from the answer of this question Mistake in derivation about categorical distribution and Dirichlet distribution? it can be shown that say $p(x|\pi)$ follows ...
3
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1answer
71 views

Learning functional analysis for studying kernels

I'm trying to learn more about kernel machine theory and I've discovered that I need to learn a lot of background math, and so I'm looking for some good resources for this. In particular: I've got ...
-1
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0answers
25 views

Joint probability and normal random variables

Say that A and B are independent and continuous random variables, and the normal distribution of A is N~(10,1), B is N~(5,2). Is the normal distribution of A and B jointly simply N~(15,3)? If no, ...
0
votes
1answer
16 views

Show that the adjusted values for 2x2 tables under the assumption of independence have the same absolute value

I am trying to show that, for 2x2 tables, under the assumption of independence, that all four adjusted residuals have the same absolute value. Adjusted residual: ...
0
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1answer
40 views

Mistake in derivation about categorical distribution and Dirichlet distribution?

$p(x|\pi)$ follows the categorical distribution (the multinomial with one observation), where $\sum\pi_i=1$ and $x$ is a one-hot vector, and $p(\pi|\alpha)$ follows the Dirichlet distribution. ...