1
vote
1answer
20 views

Determining Moving-Average Representation of AR(2) Process

Consider a stationary $AR(2)$ process given by $$X_{t} - X_{t-1} + 0.25X_{t-2} = 5 + a_{t}$$ where $a_{t} \sim WN(0,1)$ (white noise). I am interested in obtaining the causal representation of ...
1
vote
1answer
29 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
30 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 ...
0
votes
1answer
24 views

Calculating optimum values of $u$ and $m$ from $\mathbb V(\bar {y_2}\prime)=\frac{S_2^2(n-u\rho^2)}{n^2-u^2\rho^2}$

I have to find optimum sample size in sampling on two occasions. Suppose that the samples are of the same size n on both occasions. In selecting the second sample, $m$ of the units in the first ...
0
votes
1answer
32 views

Mantel-Haenszel $\chi_1^2$ statistic

I was doing a particular example from the book Epidemiologic Research by Kleinbaum(example 15.6) and didn't understood some basic statistical aspect. ...
0
votes
0answers
9 views

why not applicable categorical variables using ANOVA F or Levene test?

For independent test data is a categorical variable using the Pearson chi-squared test. But, why not applicable categorical variables using ANOVA F or Levene test? Are there any theories on this ...
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 $$\mathbb E\left[\frac{X}{Y}\right]={\frac{\mathbb E[X]}{\mathbb E[Y]}}$$ ??
2
votes
1answer
57 views

Statistical search for two needles in random haystacks

I have written a script to analyze some data at work, and for each run, it outputs a long list of integers. Each set of results is a frequency distribution (each integer appears one to many times). ...
3
votes
1answer
37 views

What is the distribution of $|X-Y|$ if both $X$ and $Y$ are $U(0,1)$?

I am trying to find the distribution of $Z = |X-Y|$ if both $X$ and $Y$ are uniform over $(0, 1)$ and independent. The answer I am getting is very close to the one given but I can't figure out why ...
0
votes
0answers
20 views

The distribution of ratio of two shifted gamma

I am wondering if anyone can help me to find the ratio of this distribution. Assume $S$ and $T$ are independent, where $S\sim Gamma(n-1/2, 4(1+\rho)\sigma^2)$ $S\sim Gamma(n-1/2, ...
0
votes
2answers
34 views

Given N-distribution, calculate expected value and Var of a function

$X_{{i}}=X_{{1}}...X_{{n}}$ is an iid. random variable with the distribution $N \left( {\frac {\alpha}{\beta}},{\frac {{\alpha}^{4}}{{\beta}^{4}}} \right) $ I would like to calculate the expectation ...
0
votes
1answer
33 views

Hypothesis testing: Test statistic, P-value and significance levels

A manufacturer claims his light bulbs have a mean life $μ = 1800$ hours. A consumer group tested a random sample of $n = 250$ bulbs and found them to have a sample mean life $\bar{x} = 1790$ hours ...
0
votes
1answer
48 views

How to bell curve

My mom is a teacher, and her kids failed a test. Suppose that her class had a mean of $x$. How would she be able to curve a the marks such that: 1) The mean is 60 2) No mark exceeds 100% Thanks
0
votes
2answers
28 views

Finding out missing observation $a$ and $b$

The mean of $a,b,8,5,10$ is $6$ and the variance is $6.8$. find out value of $a$ and $b$ I tried something like this: $$\bar{x}=6=\frac{a+b+8+5+10}{5}$$ $$7=a+b$$ Then i have put the value in ...
1
vote
2answers
28 views

Binomial/Negative Binomial Distribution? Why not Poisson here?

When I looked at the below problem, I thought of Poisson immediately. I converted the rate to making 9/10 shots. However the answer told me to use the binomial/negative binomial distribution for parts ...
0
votes
0answers
33 views

Minimizing variance of difference of two means in one-way ANOVA

From Kutner et al, fifth edition, p. 772: Refer to Rehabilitation therapy Problem 16.9. The sample sizes for below-average, average, and above-average physical fitness groups are to be $n$, $kn$, ...
2
votes
1answer
76 views

-ln(0.1) equalling to ln(10)?

I am having quite a headache wrapping my head around this solution. I do not understand the first line where they get lambda = ln(10) from statement to the left. Somebody please explain this to me. ...
0
votes
1answer
28 views

Quick Bayes Question

I drew a tree diagram but I can't get the right answer listed below. Can anyone show me how to do this? The New York State Health Department reports a 10% rate of the HIV virus for the “at-risk” ...
1
vote
1answer
43 views

What distribution should I use?

Being really bad in Statistics, need some help here. The problem is : We draw a sample of 20 laptops from a population of 1000 Laptops (serial numbers from 9000-9999). a. What distribution should i ...
-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 ...
2
votes
1answer
107 views

FIFA Probability Problem

I'm honestly unsure on how to go about this, so can anyone help me out please? There are 32 teams competing in the upcoming World Cup. These 32 teams come from five different continents: Africa, Asia, ...
0
votes
1answer
37 views

Finding probability density function of a linear combination of mutually independent normal random variables

I'm finding the probability density function of the random variable U defined in the following manner: $$U=\frac{1}{2}(Y_1+3Y_2)$$ CORRECTION: The line above is supposed to be ...
0
votes
0answers
27 views

Unbiased estimator for geometric distribution for $e^\theta$

I want to find unbiased estimator of $e^\theta$ for geometric distribution P(X = k) = $\theta (1-\theta)^{k-1}$. Sample consists of 1 element $X_1$. We can't use maximum likelihood here to find any ...
1
vote
2answers
161 views

Binomial coefficient question? Part D?

Jinbao produces tubas and ships them in lots of twenty. Suppose that 60% of all such lots contain no defective tubas, 30% contain one defective, and 10% contain two defectives. Now ...
1
vote
1answer
31 views

Statistcs Wage Problem

I need some help on how to solve this question, what approach or rules to use? Im not really sure. Do I need to use hypothesis testing? A company director took a sample of salaries of 13 employees ...
1
vote
1answer
33 views

Set Questions? Need someone to help show

I tried doing these and I have the answers, but I can only do A. Can someone show me how to do the rest? I have the answers but don't know how to get to them..
0
votes
1answer
39 views

CDF or transformation method

given $ f_(xy)(x,y)=\frac{2}{x^2y^2}$ with $x\in[1,\infty)$ and $ 1\leq y \leq x$ what is the pdf and cdf of $w = \frac{Y}{X}$ now the book tries and handles this via the so called CDF method, using ...
0
votes
1answer
52 views

A committee requires one accountant, two marketing agents..

A committee requires one accountant, two marketing agents, and four board members. If there are four accountants, three marketing agents, and seven board members available for selection in the ...
0
votes
1answer
28 views

statistics confidence level

A survey was carried out to find out if the occurrence of different kinds of natural disasters varies from on part of the town to the other. The town was divided into two as center town and town ...
0
votes
3answers
67 views

Hypothesis Testing, paired mean

I am kind of stuck on this question, I don't really know how to approach it and I would appreciate some help. The number of crime incidents during a period of 10 years were recorded in a certain ...
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
1answer
28 views

P-P plot and Q-Q plot

How to draw P-P plot and Q-Q plot manually ? I have looked at different site and they explained in various way, such as one said for p-p plot in X-axis there is residual in ascending order and in ...
0
votes
0answers
30 views

If $\rho_{12}$ =0, show that $X_1$ and $X_2$ are independent.

Suppose $X_1$ and $X_2$ are jointly normally distributed random variables with joint probability density function $f_{x_1x_2}(x_1, x_2) = \frac{1}{2 \pi ...
0
votes
2answers
30 views

Showing $Cor(X,Y) = 1$ if $a>0$ and $-1$ if $a<0$

Suppose X and Y are random variables such that $Y=aX+b$ and $a$ and $b$ are constants. Show that $Cor(X,Y) = \begin{cases} +1 &\mbox{if } a > 0 \\ -1 & \mbox{if } a < 0. \end{cases}$ ...
1
vote
0answers
15 views

Normal Approximation to Binomial Distribution using Moment Generating Functions

We're told not to use the central limit theorem to show that the normal approximation is suitable for a binomial distribution when n tends to infinity. I've managed to show the answer, but it ...
2
votes
1answer
25 views

Showing correlation is between $-1$ and $1$

If $X_1$ and $X_2$ are random variables, then $E(X_1^2)E(X_2^2) \geq [E(X_1X_2)]^2$ by Schwarz's inequality. Use this fact to show that $-1 \leq \rho_{12} \leq 1$. I know that $\rho_{12} = ...
-1
votes
2answers
51 views

find the mean value of x if The probability distribution of a discrete random variable x is given

The probability distribution of a discrete random variable x is $$f (x)= \begin{pmatrix}3 \\ x \end{pmatrix} (1/4)^x (3/4)^{3-x} $$ Find the mean value of x. Construct a cumulative distribution ...
0
votes
0answers
9 views

Extracting prediction interval data from regression print-out

On exams we're frequently given regression data print outs from matlab or whatever and then asked to construct prediction intervals for the model, getting the familiar $\frac{Y_0 - ...
0
votes
0answers
20 views

95% confidence interval for $X\sim \text{BIN}(30,\frac{1}{2})$

THe exact question is : Construct an interval in which a $Bin(30, \frac{1}{2})$ distributed X is contained approx. 95% of the time Now my first instinct was to use $\frac{X-\mu}{\sigma} \sim ...
0
votes
1answer
26 views

Binomial Distribution; Using a mean to suggest probability of success.

and thanks for taking the time to look at my question. This was for a homework task, on binomial distribution, which i thought i understood. A consignment of china mugs is packed for ...
0
votes
2answers
52 views

Calculating a Fisher expected information

Let $X_1,..., X_n$ be a random sample from a distribution with probability density function $f(x;\theta) = (1/2\theta) exp(-|x|/\theta)$ for $-\infty<x<\infty$. (a) Find the maximum likelihood ...
0
votes
2answers
53 views

What is the probability that a randomly selected 18-ounce bag of chocolate chip cookies contains fewer than 1300 chocolate chips?

I have no idea where to start on this question or where to begin to find the answer. And I'm not sure how to calculate the probability. Here is the full question: The number of chocolate chips in ...
2
votes
1answer
53 views

Power of a statistical test

I was working on the following problem: Consider two probability density functions on $[0,1]: f_0(x) = 1$, and $f_1(x) = 2x$. Among all tests of the null hypothesis $H_0: X \sim f_0(x)$ versus the ...
0
votes
0answers
18 views

Finding suitable distribution in R

I have a time serie of 100 years with daily maximum rainfall amount of every year. I have to paste a suitable distribution of daily maximum rainfall for, then use this to give an estimate based on ...
2
votes
2answers
32 views

A random variable $X$ with differentiable distribution function has a density

Setting: My professor defined A random variable $X: \Omega \to \mathbb{R}$ has a density $f:\mathbb{R} \to \mathbb{R}$ if for all $B \in \mathscr{B}$ $$P(X^{-1} (B)) = \int_\mathbb{R} ...
1
vote
0answers
25 views

Probability equations

Sorry, I wasn't sure what to name this one. I have the following assigned problem, and I am not entirely sure how to attack it: Let $A_1 = B_1^2$ and $A_2 = B_1 B_2$, where $B_1$ and $B_2$ are two ...
1
vote
1answer
27 views

Finding the marginal density of $ce^{-x^2-y^2-xy-x}$

In my probability class, we've started studying joint distrubutions and I've been tasked with the following problem: Let $(X,Y)$ have joint density $ce^{-x^2-y^2-xy-x}$, where $c>0$ is some ...
2
votes
5answers
239 views

Find the distribution of $X_1^2 + X_2^2$? [duplicate]

Let $X_1$ and $X_2$ are independent $N(0, \sigma^2)$ which means (mean = 0, variance = $\sigma^2$) random variables. What is the distribution of $X_1^2 + X_2^2$? My approach is that $X_1\sim N(0, ...
1
vote
0answers
32 views

Bivariate Correlation Unique solution

I have a set of data, let's say "score vs loss ratio", the score is an arbitrary number I gave to a team by looking at their past history. I want to prove my hypothesis which is higher the score, high ...
0
votes
1answer
51 views

Puzzle for Applying the Definition to a t distribution

The coeffcient of variation (CV) for a sample of values $Y_1,\ldots, Y_n$ is defined by $$ CV = S/ \bar{Y}.$$ Let $Y_1,\ldots, Y_n$ be a random sample of size $10$ from a normal distribution with mean ...