# Tagged Questions

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### Sufficient statistic

Let $\mathbf{X}=(X_1,\ldots,X_n)$ with joint frequency function $f(\mathbf{x};\theta_1,\theta_2)$ where $\theta_1,\theta_2$ vary independently. The set ...
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### How to estimate $\sum_{x=1:n}{xf(x)}$ having $\tilde{f}$

I have an estimator $\tilde{f}(x)$ whose error is at most $\epsilon$, i.e., $\frac{|f(x)-\tilde{f}(x)|}{|f(x)|} \leq \epsilon$. I want to estimate $\sum_{i=1:n}i.f(i)$ with a small error. But if I ...
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### My data is not normally distributed: what can I do to estimate a tail probability?

Continuing on from my earlier question, I'm attempting to analyse the data qualitatively. In the following plot, I make $10000$ samples where I count "the number of clashes". I plot $n$ vs. the ...
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### regression problem

Regression was estimated using OLS. We get y=a0 + a1x1 + a2x2 + error term. We know covariance matrix ∑ of our estimator. 1. How to get confidence interval for a1/a2 ratio? 2. In what case would ...
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### Estimating the accuracy of precipitation odds.

Modern weather forecasts often include a percentage chance of rain. If this estimate was a constant it would be a simple matter of calculating the ratio. But the reality is quite another. This is the ...
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### OLS estimators in stationary process

Given a stationary process xt=a+b*t+et with et a white noise, how can I find the OLS estimators for a and b? Cheers
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### Estimation solving for binomial k?

Hello all trying to do an estimation problem at work and wondering if I'm on the right track! I'm running a study and its on the internet. I'm trying to determine how many people I need to show an ...
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### Probabilities and Estimation of average and standard deviation

I've done a good bit of this number but I have trouble with part 2. I'll show you my work and the questions I can't figure in bold. A guy has a machine that scans his apples. The machine rules are : ...
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### How to call $(E\hat{x} - x)^2$?

Let $\hat{x}$ be an estimation of $x$. Quantity $E(\hat{x} - x)^2$ is called Mean Squared Error. How one would call $(E\hat{x} -x )^2$?
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### MMSE estimate for scalar gaussian & uniform prior

I am trying to analyze the behavior of an MMSE estimator given Guassian measurement with scalar variability on an underlying uniform prior distribution. The measurement is generated according to the ...
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### Why does maximum likelihood estimation for uniform distribution give maximum of data?

I am looking at parameters estimation for the uniform distribution in the context of MLEs. Now, I know the likelihood function of the Uniform distribution $U(0,\theta)$ which is $1/\theta^n$ cannot ...
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### Calculating a metric to compare multiple posterior probability distributions

I am beginner in mathematics/statistics and apologise in advance for my faulty use of language. Especially because I assume this to be a simple problem. I am working on a problem in statistical ...
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### 95% confidence interval around sum of random variables

Suppose I have two random variables, $X$ and $Y$. Suppose $X$ is normally distributed, and therefore I know how to compute a 95% confidence interval (CI) estimator for $X$. Suppose that $Y$ is not ...
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### What is $E[T^2]$ of $T=\frac{1}{N}\sum\limits_{n=1}^N (X[n]+W[n])^2$ ??

What is second moment i-e $E[T^2]$ of random-variable: $T=\frac{1}{N}\sum\limits_{n=1}^N (X[n]+W[n])^2$, Where $X[n]$ and $W[n]$ are both 'independent' of each other and 'stationary'. Moreover, ...
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### How to find $X_i$ from this equation

Suppose $X_i=\nu_i+\frac{m-i}{m}X_{i+1}+\frac{i}{m}X_{i-1},\quad 1\le i\le m$ where $X_0=X_{m+1}=0$. I need to find an expression for $X_i$ in terms of $v_i$, $i$, and $m$. I know how to find it ...
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### Calculating a sample's representativeness to confirm/refute a given hypothesis?

Why hello! I'm fairly new to statistics, which is why I'm somewhat confused as to how I can approach this problem in a scientific way. The problem: Experiments are conducted to find the probabilities ...
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### Unbiased Estimator Question and Understanding

I'm having some difficulty with unbiased estimators, and wondered if anyone could help me. I believe I understand the general concepts OK, however when I come to look at some sample questions to test ...
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### Density estimation for two sets of samples

Imagine two sample sets $A$ of size $\#A$ and $B$ of size $\#B$. First density estimation for both is done separately which yields $P_A$ and $P_B$ based on those densities. In what way is ...
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### square root estimator

Let's say we want to do an estimation using iid samples $X_i, i=1,2,3,..., N$ the following formula, $$\hat{X}_1 = \frac{1}{N}(\sum_i\sqrt{X_i})^2$$ square sum of square roots. This form also seems ...
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### How to find conditional distribution of outputs given input

Suppose we have a training dataset $x_1, y_1, \dots, x_T, y_T$. Our goal is to empirically estimate $P(y|x)$ using histogram of data. What histogram should I exactly use? One option is to use the ...
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### What is $\sum\ln{(x_i!)}$?

I started learning statistics and in my homework i should find the Maximum Likelihood Estimate. The function is $f_x(x)=e^{-\lambda n}\prod_{i=1}^n \frac{\lambda^{x_i}}{x_i!}$ Now i take the ...
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### Method of Moments and Maximum Likelihood estimators?

The random variables $X_1,...X_n$ are independent draws from continuous unifirm distribution with support $[0,\theta]$. Derive a method of moments and maximum likelihood estimators of $\theta$. Your ...
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### What is the probability of the number 1 and number 2 employees getting the bonus at a call center?

Two weeks ago, a friend working at a call center told me about their staff bonus policy. Here I paraphrase it. Suppose employee A answers the maximum number ($N_1$) of calls among the staff, and ...
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