0
votes
1answer
26 views

Variance- covariance matrix

Consider $H$ denotes hat matrix and $e$ denotes residual. In the book Applied regression Analysis by Draper/Smith, it is written that : $\mathbb V(e_i)$ is given ...
0
votes
1answer
24 views

Confidence Interval for Regression Coefficient ,$\beta$

In the book 'Applied regression Analysis' by Draper/Smith, it is written that : Obtain individual $100(1-\alpha)\%$ confidence interval for the various parameters separately from the formula ...
2
votes
4answers
124 views

Is it true that $\mathbb E[{\frac{X}{Y}]}={\frac{\mathbb E[X]}{\mathbb E[Y]}}$?

If $X$ and $Y$ are both random variables, does it hold $$\mathbb E\left[\frac{X}{Y}\right]={\frac{\mathbb E[X]}{\mathbb E[Y]}}$$ ??
-1
votes
1answer
20 views

Probability in a Random Sample [closed]

V. The mean monthly rental rate for a two-bedroom apartment in Atlanta is $\$982$ (Elle. September 1998). Assume that the population mean is $\mu = \$982$ and the population standard deviation is ...
0
votes
1answer
21 views

Consequences of violation of independence assumption in ANOVA test

Can you please explain me what is the consequences of violation of independence assumption in ANOVA test? I couldn't visualize it. Does Cochran Theorem relates to ...
0
votes
0answers
16 views

Calculating person-time

Suppose that an investigator wants to measure the incidence rate of high blood pressure in the $1997-98$ freshman class of a university. Assume that there were $1000$ entering freshmen and that this ...
0
votes
1answer
39 views

the random heights of north american women

The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches. A random sample of four women is selected. What is the probability that the ...
0
votes
1answer
49 views

Sampling without replacement

I've recently started studying statistics again, and I've just come across sampling without replacement. My book states that if we have a elements of type I and b elements of type II, then the ...
0
votes
0answers
21 views

Taylor Series Expansion for Sampling Theory

There is a question which I am not particularly comfortable with doing. It is related to the Taylor Expansion for Random Variables: Let $\overline{y}_S$ and $\overline{x}_S$ be sample means, $m = ...
1
vote
1answer
104 views

What proportion are above x of sample size n where X ~ N(0,1) Homework

I have a homework question that I'm not quiet sure of. It follows as so: Consider a random variable $X$ that has a standard normal distribution with mean $\mu=0$ and standard deviation $\sigma=1$. ...
1
vote
1answer
96 views

Required sample size to reduce the interval size by half

I have a small doubt regarding a statistics problem and would like a confirmation. If we want to reduce the length by half of the confidence interval (at 95%), we should: Multiply the size of the ...
0
votes
2answers
79 views

Probability that I am not selected in any of 2000 samples?

The population contains 100 million adults, which includes myself. Simple random sampling is used to choose a sample of 1000 adults, 2000 times, independently. I need to find the probability that I ...
1
vote
1answer
57 views

Calculate each point of my Gauss curve

I'm coding a program which calculates the confidence interval. He takes the population and a sample of the population as parameters, and the percent of people of that sample who answered "yes" to a ...
0
votes
1answer
216 views

please prove the following proof related to F distribution.

Suppose $S_1^2$ and $S_2^2$ are two independent unbiased estimate of the common population variance $\sigma^2$ from two random sample of sizes $n_1$ and $n_2$ respectively. Then show that ...
2
votes
1answer
104 views

Monte Carlo Rejection Sampling Method

I have the following passage from a set of lecture notes I am working on that I would like to understand a little better. $\underline{\text{Algorithm for Rejection Sampling}}$: Given two densities ...
2
votes
1answer
469 views

unbiased estimator of sample variance using two samples

I have a couple questions, I'm hoping someone can help! Let $X_1...X_n$ is a random i.i.d. sample from a $N(\mu,\sigma^2)$ distribution, and $Y_1...Y_m$ is a random i.i.d. sample from a ...
0
votes
0answers
149 views

Giving sampling distribution of population total estimator [Homework]

Given sampling data below, Considering a Simple Random Sampling(SRS without replacement) of size 4, what is the sampling distribution of the estimators for total of y's? t1 and t2 where i) t1 is ...
2
votes
1answer
89 views

$\chi^2$ test and sampling variance

Let $f(x)$ denote the pdf of a $\chi^2$-distribution with $n\in\mathbb{N}$ degrees of freedom given by $$f(x) = \frac{2^{-n/2}}{\Gamma(n/2)}\cdot x^{n/2-1}\cdot\mathrm ...
4
votes
3answers
332 views

What is “sampling from a distribution”?

Exercise 4.11.3 of Grimmett and Stirzaker's Probability and Random Processes reads "Use the rejection method to sample from the gamma density $\Gamma(\lambda,t)$ where $t (\geq 1)$ may not be assumed ...