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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21 views

demostrate Jensen's inequality (i think)

Please any help is very good. I was trying to start with the definition of expected value but I don't know how to finish.
2
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0answers
12 views

Error of bounded mean estimation with quantization

I have a distribution whose mean $\theta \in [0,1]$. Given $n$ observations, I compute the sample mean (say $\hat{\theta}$) and quantize it to accuracy $\frac{1}{n}$ (basically I can use only ...
1
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0answers
19 views

Sufficient and complete statistic

Let $ X_1, ... , X_n $ be i.i.d random variables with pdf given by $$f(x;\theta) = \exp(-(x-\theta))I_{(\theta, \infty)}(x)$$ It is asked to find a sufficient statistics for $ \theta $ and to verify ...
-1
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0answers
44 views

Calculate the mean and variance of two random variables from their density functions

How do you calculate the mean and variance of two random variables X~F(m = 3, n = 6) and Y~F(m = 8, n = 6) from their density functions using R?
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1answer
19 views

Conditional Binomial Question

Lost touch on some basics: $X \in Bin(n,p)$. Suppose that we know $P(X \ge l)$. Can we get a distribution for $P(X=x | X \ge l)$, $l \le n$? I would assume we use bayes rule and find $P(X=x, X \ge ...
3
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1answer
25 views

Question about definition of random sample

In my statistics class, we're just beginning to talk about (point) estimation. I have a small question that might actually be due more to notation/definition than anything very conceptual: Say you ...
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0answers
16 views

how one independent variable affects other variable in multiple regression

I have a two independent predictors in regression equation "X1" and "X2". X2 is categorical hence 1,0 is the allowed values. I have to find how X1 get affected based on value in X2 in following ...
0
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1answer
22 views

Probablity calculation for at-least clause case

I saw the question: What is the probability of 1 out of 5 randomly selected people agree with the statement that men having more right for job compare to women? ...
0
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1answer
28 views

Find MLE by combining two different experiments

I am trying to solve the following problem on an assignment. Anna has two dice. Die $F$ is fair: it rolls $1,2,3,4,5$ or $6$ with equal probability $\frac{1}{6}$. Die $D$ is dodgy: Anna suspects ...
4
votes
1answer
83 views

null hypothesis change

I've done loads of hypothesis tests for the mean (normal distribution) where the null hypothesis is of the form $H_{0}=a$. Now I've come across one where the hypotheses are like $H_{0}{\leq}a$ and ...
0
votes
1answer
51 views

Homework problem. What is the answer supposed to look like?

I am taking a statistics course this semester, and this is part of our first homework assignment, only I don't know what the answer is even supposed to look like. When the process is functioning ...
2
votes
1answer
53 views

Design of Experiments

Suppose a dermatologist wants to study the effectiveness of two different preparations of a skin lotion using two different forms of application, such as one versus two applications per day. She has ...
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0answers
24 views

How do the various distributions work into machine learning

I'm a student who recently started taking a machine learning course and I'm trying to understand how the various distributions fit into the whole thing. From the research I've been doing it seems the ...
2
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1answer
51 views

What is the name of the distribution of unbiased sample variance for a sample from Gaussian distribution?

Suppose $X_i$'s are iid Gaussian random variables with mean $\mu$ and variance $\sigma^2$. The distribution of $\sum_i (X_i - \bar{X}_i)^2 / (n-1)$ isn't Chi square. What is its distribution called? ...
1
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0answers
16 views

Sample of one, extermination of fruit flies and daily life challenges

First of all, I'm very well aware that a sample of one is ridiculous in any normal scenario in the domain of statistics, and I know that any rationale from this would probably only have esoteric ...
1
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0answers
13 views

Fractional Factorial Design with Highest Resolution

In the book Design and Analysis of Experiments by Douglas C. Montgomery , it is written that We usually like to employ fractional designs that have the ...
2
votes
1answer
103 views

drawing balls from an urn

Suppose there are 7 golf balls in an urn and you draw balls in 3 stages without replacement. First you draw 2, then 3, and then the remaining 2. How many ways are there to do this? I believe the ...
3
votes
1answer
36 views

Covariance of $cov(5W_7+6W_9,W_7)$ where $W_t$ is a standard Brownian motion

I'm having trouble deducing the value for the problem in the title. Here is what I have done so far. (Given a standard Brownian motion (BM) $W_t, t\geq0 $ with $W_0 = 0$ and $\sigma^2=1$) The ...
3
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0answers
51 views

How to find an appropriate sample size given information about the CV?

You are planning to collect a (simple random) sample to estimate the mean of a non-negative random variable. It is known that the population coefficient of variation (CV) is 1.2. Use the central ...
2
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0answers
34 views

How to answer a clients question on “How accurate your logistic regression model is?”

There are various methods to test the model accuracy, but when it comes to clients you may face people who don't know AIC, ks-statistic, c statistic, confusion matrix, etc. So, how one should answer a ...
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4answers
1k views

How to add odds? (or how I got the wrong sandwich)

Jon and Frank ordered 2 footlong sandwiches, but instead got 4 6-inch sandwiches. Jon had ordered spicy italian, and Frank chicken teriyaki. The sandwiches aren't labeled and are wrap, so they can't ...
0
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0answers
12 views

Plotting of density estimates in matlab [migrated]

Given the biometric match scores, I am required to plot the graphs of estimated densities of matching genuine and impostor scores. Following are the graphs I got for genuine and impostor scores ...
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0answers
29 views

A non-negative definate matrix has a non-negative generalized inverse

I'm having trouble proving a N.N.D matrix has a N.N.D G-Inverse. So far I have: If we assume x = Az where x >= 0 and A is a nnd matrix. So if Y is a G-inverse than: x = Az = YAz = Yx >= 0 . Thus ...
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0answers
25 views

What method should I use to analyze data? [closed]

I failed to pass my regression analysis course as the lecturer didn't say what kind of analysis he wants on the data. The problem was: The index of biotic integrity (IBI) is a measure of the water ...
1
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1answer
40 views

Sum of Random Variables

As part of my statistical mechanics class, I'm trying to go through Kardar's statistical physics of particles and I'm having trouble with this one line: Consider the sum $X=\displaystyle ...
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0answers
49 views

Problem solving a simple probability exercise

I'm currently studying a Statistics course and I'm trying to solve a simple probability exercise: A production facility employs: 20 workers on the day shift 15 workers on the swing shift 10 workers ...
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0answers
56 views

Gini index vs entropy

If I have a discrete probability distribution $p$ with $K$ classes Gini index = $\sum_{K}$$p_k$(1-$p_k$) Entropy = -$\sum_{K}$$p_k$log$p_k$ Per 'The Elements of Statistical Learning', ...
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1answer
57 views

How to solve the attached question?

Any help for solving the attached question (b), (c), (d) and (e) is appreciated.
0
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1answer
25 views

Fractional Factorial Design

In a $2^5$ design, it is believed that only the main effects $(A,B,C,D, E)$ and $AB,AC$ interaction effects are non-zero. I need to construct a fractional factorial with minimum number of runs which ...
3
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0answers
55 views

Unbiased estimator with minimum variance for $1/\theta$

Let$ X_1, ...,X_n$ be a random sample feom a distribution $Geometric(\theta)$ for $0<\theta<1$. I.e, $$p_{\theta}(x)=\theta(1-\theta)^{x-1} I_{\{1,2,...\}}(x)$$ Find the unbiased estimator ...
2
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2answers
65 views

Skewness of a random variable that have zero variance and zero third central moment

If I have a random variable $x$, and the only information I know about it are: $$ m_1=E[x]=c, \mu_2=var(x)=0, \mu_3=E[(x-m_1)^3]=0$$ Can I conclude that the function distribution is symmetric about c? ...
0
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1answer
26 views

$2^{5-2}$ Design : Alias Structure

$2^{5-2}$ Design Design Generators: $D=AB\quad E=AC$ Defining Relation: $I=ABD=ACE=BCDE$ $$\text{Aliases}$$ $$A=BD=CE=ABDE$$ $$B=AD=ABCE=CDE$$ $$C=ABCD=AE=BDE$$ $$D=AB=ACDE=BCE$$ ...
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2answers
72 views

Identifiability of normal distribution

I am working on an exercise problem and am stuck in this problem: Suppose that $X_1,\dots,X_n$ are independent with $X_i\sim\mathrm{N}(\alpha_i + \nu, \sigma^2)$. Let $\theta = (\alpha_1, . . . , ...
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0answers
10 views

Sample autocovariance non negative definite

Let $\hat{\Gamma}_k$ be the k dimensional sample autocovariance matrix. I am trying to prove this is nonnegative definite. The first step in the proof is to show that if $\hat{\Gamma}_m$ is ...
0
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0answers
17 views

confidence level query

A new treatment for strokes is put on trial. There are two equal size groups,one group is given a drug, and one a placebo. The 95% confidence interval for the difference between the two proportion of ...
17
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9answers
1k views

What is the relationship between $Y$ and $X$ in this plot?

What is the relationship between $Y$ and $X$ in the following plot? In my view there is negative linear relationship, But because we have a lot of outliers, the relationship is very weak. Am I right? ...
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2answers
89 views

Sum of combination

My problem is: Evaluate: $$\sum_{i=0}^n i{n \choose i}$$ I only know that $$\sum_{i=0}^n{n \choose i} = 2^n$$ not so sure when an "i" is added. What is the step of this evaluation?
3
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1answer
67 views

Unable to understand derivation of Expectation Maximizaton

In Paper, System Identification using Symbolic Chaotic Sequence, Authored by A. Kurian and H. Leung download link under section II B, can somebody please explain ...
4
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0answers
91 views

Suppose that A and B are mutually exclusive events for which P(A) = .3 and P(B) = .5

Suppose that A and B are mutually exclusive events for which P(A) = .3 and P(B) = .5. What is the probability that ...
5
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2answers
90 views

Maximum likelihood estimator for $\theta$ and $E[X]$

Let $X_1,..., X_n $ be a random sample of a variable with PDF: $$f(x|\theta)=\frac{\theta}{x^2} I_{(\theta, \infty)}(x), \theta >0$$ Find the maximum likelihood estimator for $\theta$ and $ E[X]$ ...
1
vote
1answer
26 views

Autocorrelation summation identity

Let $X_t$ be a weakly stationary process with mean $\mu$ and autocovariance function $\gamma$. How do I show that $$n^{-2}\sum_{i=1}^n \sum_{j=1}^n cov(X_i, X_j)$$ equals $$ n^{-2} \sum_{i-j=-n}^n ...
2
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2answers
61 views

How can I calculate t-score without knowing true population mean?

I am studying now t-scores. As far as I understand, t-scores are used when we don't know true population parameters (such as: standard deviation and population mean) and cant use z-scores. Here is ...
1
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0answers
35 views

Probability that one person's weight is more than 50 pounds greater than another's

The weight of a Portuguese man is normally distributed with mean 160 pounds and standard deviation 30 pounds. The weight of a Portuguese woman is normally distributed with mean 120 pounds and ...
1
vote
1answer
60 views

Using chi goodness of fit to test if data comes from normal distribution

The problem gives 50 observations and then asks to check whether the data comes from a normal distribution. For instance if these are your observations then how would you go about testing to see if ...
1
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0answers
30 views

Three Events Problem Interpretation

So I am having trouble understanding what this problem is asking. (I am not asking someone to solve it but simply help interpret what the problem wants me to do.) The problem goes like this: "Let ...
4
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0answers
48 views

Cantelli's inequality proof

I am trying to prove the following inequality: EDIT: Almost immediately after I posted this question, I discovered that the inequality I am being asked to prove is called Cantelli's inequality. When ...
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0answers
9 views

Estimating Probabilities from Stratified Table

Say I have data stratified by smoking status, where $Y=1$ is has lung cancer, $Y=0$ doesn't have lung cancer, and finally $D=1$ drinks alcohol, and $D=0$ doesn't drink alcohol. How do I estimate ...
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0answers
56 views

Treating Categorical Data as nominal or ordinal? [duplicate]

There is a four category classification system for individuals with HIV, labeled Stages 1, 2, 3, and 4, with higher stages indicating more advanced disease. Cell count is a continuous variable, and ...
2
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1answer
62 views

Linear Regression with Dummy Predictor

Say there are two groups, each with n=500, with y=weight in pounds. The sample mean and sample standard deviation of weight are given: Exercise(X=1): Mean=170, SD=20 Non-Exercise(X=0): ...
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3answers
86 views

Beyond the basics: intermediate medical statistics textbooks suggestions

I am a soon-to-be physician. During my studies I have taken a class in biostatistics. I own Martin Bland's "An introduction to medical statistics", which was a required textbooks at the time, and ...