1
vote
1answer
47 views

Find an unbiased estimator

Let $X$ be an r.v defined by $P(X=0)=p$ and $P(X=1)=1-p$. Find an unbiased estimator for $2p$. My solution: $E(X)=1-p$ so $2-2E(X)$ is unbiased. Is this correct?
0
votes
1answer
63 views

Determine the Asymptotic Distribution of the Method of Moments Estimator of $\theta$, $\tilde{\theta}$

I am having difficulty understanding what it means to find the asymptotic distribution of a statistic. I have the correct answer (as far as I know), but I am unconvinced that I understand the process ...
1
vote
1answer
54 views

Rolling a die 100 times and adding results

Simple problem. We role a die 100 times and we add the results. What is the probability of getting sum between 330 and 380 ? I got this: $P(330 \le X \le 380) = P\left( \frac{330 - n * ...
0
votes
1answer
36 views

proving unbiasedness of an estimator

Question given independent random variable $X_{1},X_{2},...,X_{n}$ from a geometric distribution with parameter $p$. we have an estimator for $p$, mainly $T=Y/n$ where Y is number of $i$ that ...
0
votes
0answers
20 views

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 ...
0
votes
0answers
12 views

What is the variance of the largest sample among a set of independent samples?

Say x1, x2, ..., xn are independently derived from a uniform distribution [0, d] (or any other kind of distributions). What will the variance of max(xi) be? Does it follow some sort of distribution ...
0
votes
0answers
47 views

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 ...
1
vote
1answer
153 views

Weibull Scale Parameter Meaning and Estimation

Wikipedia: http://en.wikipedia.org/wiki/Weibull_distribution gives a nice description on what the shape parameter (they call it k) means in the Weibull distribution, but I can't find anywhere what the ...
2
votes
1answer
96 views

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 ...
2
votes
0answers
109 views

Cramer-Rao bound for $\chi^2$ distribution parameter estimates.

I've stuck in unpleasant problem with noncentral $\chi^2$ distribution. I work with random variables, distributed as $\chi^2_{\nu}(\lambda)$, where $\nu$ is the degree of freedom and $\lambda$ is ...
1
vote
1answer
370 views

Sufficiency and UMVUE for Poisson distribution

I need to show that $\hat\lambda = \bar X$ is a sufficient estimator for a Poisson distribution iid $X_1...X_n$, show that $\hat\lambda$ is the UMVUE for $\lambda$ and that $\hat\lambda$ is a ...
2
votes
1answer
39 views

Multi-dimensional MLE Guassian

I wonder that what is the mu and sigma formula MLE(maximum likelihood estimates) for a 3 dimension guassian ? It is the same form as 1 and 2 dimension (+ 1 mu and sigma for the new vector) ?
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votes
1answer
264 views

Expected value for the number of goals in a game

I'm trying to use odds data from bookmakers to estimate the expected number of goals in a game. We have these known facts: P(o4.5) = 0.573 P(o5.5) = 0.458 P(o6.5) = 0.279 P(o4.5) is the ...
2
votes
1answer
941 views

How to efficiently estimate quantile function of Gamma distribution

I have an application that analyzes datasets comprised mostly of samples from a Gamma distribution. Mixed in with the data are an unknown number ($>= 0$) of outlier samples (which are actually taken ...