0
votes
0answers
42 views

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 : ...
0
votes
0answers
50 views

Covariance of $(\bar{X}, \bar{Y})$ under Simple Random Sampling

$\newcommand{\Cov}{\operatorname{Cov}} \newcommand{\Var}{\operatorname{Var}}$ Under Simple Random Sampling without replacement, and two variables of interest $X$ and $Y$, want to estimate "$r=Y/X$". ...
1
vote
1answer
41 views

Overestimate of $|\oint_{|z|=R} f(z) \mathrm{d}z|$ with $f(z)=\frac{z^a}{z^2+1}$, $0<|a|<1\mathrm{with} \;a \in \mathbb R$

How can I overestimate, $|\oint_{|z|=R} f(z) \mathrm{d}z |$ with $f(z)=\frac{z^a}{z^2+1}$, $0<|a|<1 \; \mathrm{with} \;a \in \mathbb R$ ? I tried this: $|\oint_{|z|=R} f(z) \mathrm{d}z | <= ...
1
vote
1answer
61 views

Advanced urn problem

Imagine there are two urns — urn A and urn B. Urn A contains 3 blue balls and 7 red balls. Urn B contains 7 blue balls and 3 red balls. Balls are now randomly drawn from one of these urns where the ...
1
vote
1answer
81 views

Find $\sin(1/10)$ to within error of $10^{-7}$

The maclaurin series of $\sin(x)$ is $x- x^3/3! + x^5/5! - \cdots + (-1)^n x^{2n+1}/(2n+1)!$. My teacher wants me to use Taylor's inequality theorem on page 607 to solve this problem. I know that ...
0
votes
1answer
107 views

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 ...
0
votes
1answer
57 views

MLE problem - the likelihood function has no maximum.

The probability density function is: $f(x)=e^{\theta -x}, \ 0 \le \theta \le x $ Given an n-element sample, the likelihood function is: $$L(\theta)=\exp \left( n\theta - \sum_{i=1}^n x_i \right)$$ ...
0
votes
1answer
41 views

MLE estimation for number of customers.

A clerk in a shop has noticed two customers arrived at the shop between 12:00 and 12:45. Another clerk noticed only one customer between 12:15 and 13:00. Assuming a Poisson distribution on the number ...
3
votes
2answers
2k views

Maximum likelihood estimation of $a,b$ for a uniform distribution on $[a,b]$

I'm supposed to calculate the MLE's for $a$ and $b$ from a random sample of $(X_1,...,X_n)$ drawn from a uniform distribution on $[a,b]$. But the likelihood function, ...
1
vote
1answer
361 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 ...
1
vote
1answer
77 views

How do I use student's-t distribution without the sample size?

Here is my question (homework obviously): A sample from a normal population produced variance 4.0. Find the size of the sample if the sample mean deviates from the population mean by no more than 2.0 ...
3
votes
1answer
46 views

Estimate the given sum.

This is the question from "Data Structures and Algorithm Analysis in C" By Mark Weiss. It is the question 1.7. It goes as follows:- Estimate the sum ...
-1
votes
1answer
40 views

Estimate: $|f^{(3)}(i/3)|$.

Suppose $f:D(0,1)\longrightarrow \mathbb{C}$ is holomorphic, where $D(0,1)=\{z\in\mathbb{C}∣|z|<1\}$, and assume the maximum $|f(z)|\leq 2$. Estimate: $|f^{(3)}(i/3)|$. I just don't understand how ...