-1
votes
0answers
7 views

Calculate the auto correlations and mean of the following time series [on hold]

$$Y)t=0.7+0.4Y_t−1+0.12Y_t-2+Z_t$$ calculate $E(Y_t)$ Also calculate the auto correlations $p_1-p_4$.
0
votes
0answers
24 views

Which hypothesis test to use

Two identical machines are used to make a special coin. We want to know if they have the same variability. A random sample is taken from each machine : $$ \begin{matrix} MachineA & 135 & ...
0
votes
0answers
16 views

Poisson distribution confidence intervals and hypothesis

I think I have A and B correct but I have troubles with parts C and D. A) What is the p value if we suppose the following : finding golden apples in a tree follows a Poisson P(2) with $\lambda = 2$ ? ...
1
vote
1answer
16 views

Statistical Intervals - Confidence Intervals Homework Help

The following is a homework problem from my textbook, I am totally confused on how to solve this problem. Please help!!!!! Let $X_1, X_2, ………, X_n$ be a random sample from a continuous probability ...
1
vote
1answer
26 views

Question on finding the Jacobian

I have a question which is as follows: The random variable U has the pdf $n \dfrac{u^{n-1}}{\theta^{n}}$ , $ 0 \le u \le \theta$ This is not independent of the parameter θ. Let Y=U/θ. Use the ...
2
votes
1answer
38 views

Do I use the Standard Deviation of my sample or the population to find the standard error.

A professor is interested in determining if attending college influences the level at which an individual cooperates with the police. The professor is unsure if attending college will teach respect ...
0
votes
1answer
11 views

Comparision between two random samples

I have the following simple random samples which denote the scores obtained by some students over $10$: Random sample A: 3.5 4.5 4.813 5.065 5.252 5.438 5.547 5.586 5.937 6.025 6.025 6.345 6.375 ...
0
votes
1answer
30 views

Regarding jointly multivariate normal X1,X2…X5

So I have a question from statistical inference that I need some help with: $X_1,X_2,...,X_5$ are jointly multivariate normal with means = $\mu_i$, variances = $\sigma^2_i$, correlation = $\rho$ ...
1
vote
2answers
62 views

Determining constant in a CDF

I have a question that I literally have no idea how to begin, I was hoping someone could help me: It says $X_1,X_2,\ldots,X_n$ is a sample from a distribution It says that the Cumulative ...
0
votes
2answers
68 views

What is this distribution???

Let $X_1, X_2, \ldots, X_n$ be a random sample from a population with $E(X_i) = \mu$ for all $i \in \{1,\ldots, n \}$. Define $ Y_i = \begin{cases} 1 & \mbox{ if } X_i < \mu \\ 0 ...
0
votes
0answers
17 views

Signed rank test help

suppose i have 10 paired observations (which are skipped here). Suppose also that i want to test $H_0$: no difference between these distributions. Against $H_1$ they differ. that is a two tailed test. ...
1
vote
1answer
29 views

Getting the right P value

i want to check if there is a significant difference between in gasoline consumption between gas-1 and gas-2: here are some observations from gas-1 ...
1
vote
1answer
22 views

Confidence level of random sample from continuous distribution

Let X1,X2,⋯,Xn be a random sample from a continuous distribution with median μ. If [Xmin, Xmax] is used as a confidence interval for μ, what is its confidence level? What is the confidence level if ...
2
votes
2answers
28 views

Minimum of variance when sample is unbiased?

Show that if an estimator $\hat\mu=a_1X_1 +a_2X_2 +\cdots+a_nX_n$, where $a_1, a_2,\ldots,a_n$ are constants, is unbiased, then its variance is minimum when $a_1=a_2=\cdots=a_n=\frac{1}{n} ...
0
votes
1answer
23 views

Finding P value

I have these observations $(2,3.2,3.8,2.5,3.3,2.8,3.0,3.4)$ from $X \sim N(\mu,\sigma^2)$ and i want to calculate the $P$-value testing $H_0: \mu =3.2$ against $H_1 \neq 3.2$ with $\sigma = 0.6$ ...
1
vote
1answer
41 views

Upper and Lower one sided confidence level

Iam trying to calculate upper and lower confidence levels for a parameter, but i can't get it straight (in this case $\sigma^2$): the reference variable: $R_{\sigma^2} := \frac{n-1s^2}{\sigma^2} \sim ...
1
vote
1answer
104 views

Finding MLE of $f(x;\theta) =1$ if $\theta-1/2<x< \theta+1/2$

Let $X_1,...,X_n$ have density: $f(x;\theta) = \begin{cases} 1 &\mbox{if } \theta-1/2<x< \theta+1/2 \\ 0 & otherwise \end{cases}$ Let $Y_1=min \lbrace X_1,...,X_n \rbrace$ and ...
0
votes
0answers
20 views

Business Statistics

A forester measured 49 of the trees in a large woods. The mean diameteris 10.5 in. & the standard deviation is 3.1 in. What size would you expect the largest 95% of the trees to be?
0
votes
0answers
56 views

Find MLE of $\alpha$ of $f(x;\alpha)=(1+\alpha x) /2$ (stuck at derivative setup)

$X_1,...,X_n$ is an independent sample with common density: $f(x;\alpha)=(1+\alpha x) /2$ where $-1<x<1$ and $-1<\alpha <1$ I have to find the maximum likelihood estimate of $\alpha$. ...
1
vote
1answer
55 views

Inference Ph in water

This is an example from my book and Iam translating from it so there might be some things that are not all clear. Just let me know so i can edit. Someone is measuring PH-level in a sea and for that ...
0
votes
1answer
229 views

Shifted Exponential Distribution and MLE

I was doing my homework and the following problem came up! We have the CDF of an exponential distribution that is shifted $L$ units where $L>0$ and $x>=L$. The CDF is: $$1-e^{-\lambda(x-L)}$$ ...
0
votes
1answer
21 views

Easy Maximum-Likelihood problem

Problem $F(x)=x^{\alpha}$ for $0 \le x \le 1$. Where $\alpha>0$ is unknown. Observed values of x: 0,57 0,81 0,63 0,44 0,31 0,91 0,36 0,65 0,74 0,99 Do an ML estimate of $\alpha$. Attempt: I ...
0
votes
0answers
17 views

$p$-dimensional confidence set for normal linear model

this is a question about a confidence set in $p$-dimensional space for a normal linear model. If we define the cuboid $C:= \prod_{j=1}^p C_j(\frac{\alpha}{p})$, where $$C_j(\alpha) = [\hat{\beta_j} ...
1
vote
3answers
76 views

Show that the co-variance is zero between $\bar{Y}$ and $Y_i - \bar{Y}$

I have a quick question about how to mathematically show this result. Here is the question and my thoughts. Let $Y_1, \ldots, Y_n$ be i.i.d. R.Vs with mean $\mu$ and variance $\sigma^2$ and let ...
2
votes
2answers
61 views

Distribution of the sample variance

This is my first post to this great website :) It seems like an excellent place to learn. I have a question however that is bothering me as I cannot figure it out through my textbook. The sample ...
1
vote
1answer
39 views

$Z$~$N(0,1)$ relating to the chi square distribution

Let $Z$~$N(0,1)$. If I want to write down the definition of $M_{z^2}(t)$ which is the MGF of $Z^2$, I would write the following correct? $E(e^{tZ^2})$ Assuming that the answer above is correct, if ...
0
votes
1answer
52 views

Justifying the Normal Approx to the Binomial Distribution through MGFs

Would absolutely love if someone could help me with this question, in a step by step way to help those who are uninitiated to Statistics and Mathematics. So, I am trying to "prove/justify" through ...
1
vote
1answer
25 views

Morphing $\beta_1$ into a different form (OLS question in Statistics)

I am currently studying Simple Linear Regression and I have successfully proven to myself how $\beta_1$ and $\beta_0$ are derived. However, I have been stuck on a seemingly simple problem (I'm sure ...
0
votes
0answers
20 views

Suggesting a UMVU for a poisson distribution

The number of clients arriving at a certain bank in an hour poissonically distributed with $\lambda$. Suggest a UMVUE according to the following 4 observations: $12,25,18$ and $27$. I know that a an ...
1
vote
1answer
135 views

a distribution of a sqrt of a Normal distribution

i have a Normal(0,1)=X. and (X_{1},....X_{20}). I have to calculate the distribution of $T=\sqrt{|Z|}$ with Z= $\dfrac{1}{20} \sum_{1}^{20}X_{i}$ and his average. I have done this, but Im not very ...
0
votes
2answers
631 views

What situation calls for dividing the standard deviation by $\sqrt n$?

While doing my homework and checking my answers with the book's answers I noticed that sometimes the standard deviation is divided by $\sqrt n$ where $n$ is the sample size. I'm a little confused. For ...
0
votes
2answers
52 views

Finding the mean of an unknown distribution.

I solved the integral and it's theta, but i'm not sure how to get the mean of the distribution because i don't know the kind of distribution i'm dealing with. Any ideas? i'd really appreciate your ...
1
vote
1answer
69 views

When I read the question related to two population hypothesis test, how can I decide whether the population is dependent or independent?

Hi, I am studying two population hypothesis test in statistic. I added two Photos related to the topic which include the descripion of the topics. First one is related to depended sample. Second ...
0
votes
1answer
217 views

Cramer-Rao lower bound for the variance of the unbiased estimator of $\tau(\theta)$

Given the pdf $f(x;\theta)=\frac{1}{\pi[1+(x-\theta)^2]}$ ; $-\inf < x<\inf$, $-\inf < \theta<\inf$ Show that the Cramer-Rao lower bound is 2/n where n is the sample size.
0
votes
0answers
35 views

The sum of variable whith inverse Gauassian distribution

Let $ X_1,X_2,...,X_n$be a sample from inverse Gaussian pdf whith parameter $\mu$ and $\lambda$ .I want to show that $\overline{X}$ has an inverse Gaussian distribution with parameter $\mu$ and ...
0
votes
1answer
31 views

nonparametric test for sample and control

Hi I have to use an appropriate test (and justify my choice) to explore whether there is an underlying difference in location between the concentration of an Enzyme in rats exposed to a specific ...
1
vote
1answer
368 views

Rao-Blackwell Uniform Distribution

I am having a bit of an argument with my study group about a Rao-Blackwell problem that we have for our statistical theory class. The problem goes like this: Let X~U(0,$\theta$), and suppose we have ...
2
votes
2answers
483 views

Sufficient Statistic for a Geometric R.V.

I have a problem that I know I am very close to the solution for, but I think I just need some more formatting to make it a really clean proof. The problem goes like this: Suppose X is a discrete ...
1
vote
0answers
679 views

Beta Distribution Sufficient Statistic

So I have this homework problem that I am struggling a little bit with coming to a solid answer on. The problem goes like this: Suppose X~Beta($\theta,\theta), (\theta>0)$, and let $\{X_1, X_2 , ...
1
vote
0answers
35 views

Test the hypothesis that $B_1=0$ at the $5 \%$ significance level

I am told to test the hypothesis and this is what I did: $H_{0}:\beta_{1}=0$ $H_{a}:\beta_{1}\not=0$ So then I have $$t^{*}=\dfrac{\hat{\beta_{1}}-\beta_{1}}{\dfrac{s_{\beta_1}}{\sqrt n}}$$ ...
1
vote
2answers
88 views

Construct a Confidence Interval of $95\%$

Based on a random sample of 20 values from a normal distribution with mean $\mu$ and variance $\sigma^{2}$, it was calculated that $\bar{X}=8$ and $s=4$. Provide a $95\%$ confidence interval for the ...
0
votes
1answer
90 views

How to estimate parameters of a normal distribution?

Suppose one knew that 105 workers were evaluated by their boss. Such evaluation is distributed according to a normal distribution with mean $\mu$ and std. deviation $\sigma$. We also know that 20 ...
1
vote
3answers
170 views

Simple standard deviation question using stocks as example

The following table is from page 171 of Fundamentals of Investing (11th edition) by Gitman, Joehnk, Smart. Please consider only the X, Y and XY columns (second, third, fifth). Portfolio XY comprises ...
0
votes
1answer
215 views

Test for a poisson distributed random variable

I need help with the following exercise: Assume the amount of apples falling to the ground from a single tree can be modeled by a poisson distributed random variable $X$ with expectation $m$. The ...
0
votes
1answer
40 views

independence of uniform random variables1

let $X_j \sim U(0,1)$ if $$Y_j=\frac{X_j}{X_1+X_2+\cdots+X_n}$$ I want to show that: $Y_j $are independent $\operatorname{Var}(Y_1)=\dfrac{c}{n^2} +o\left(\dfrac{1}{n^2}\right)$ then calculate ...
0
votes
1answer
595 views

Confidence interval for exponential distribution

I'm having trouble with homework and hope somebody can help. The lifespan of a lightbulb is assumed to be a random variable $X$ with density function: $$f_X(x)=e^{-x/\theta}/\theta,\, 0\leq x $$ ...
1
vote
0answers
104 views

Need help deriving plug-in (functional of distribution) estimator

I need help with homework exercise, have no idea how to approach it. Assume we have i.i.d. observations $x_1,\ldots,x_n$ of a continuous random variable $X$, taking values in $\mathbb R^+$. Define ...
2
votes
2answers
165 views

expectation value 3

Suppose that $X$ is a non-negative random variable and there exist constants $A,B$ such that $$\forall t > 0\colon P(X>\frac{1}{t})<Bt $$ and $$\forall t > 0\colon E(\sin(tX))<At$$ I ...
3
votes
2answers
101 views

distribution function

Suppose that $X$ and $Y$ are two random variables such that: $$E \left(\frac{a}{a+X} \right)=E\left(\frac{a}{a+Y}\right)< \infty \qquad\forall a > \pi.$$ Can we conclude that $X$, $Y$ have the ...
1
vote
1answer
141 views

Density function and cumulative distribution function of a random variable

Suppose that $X_n$ is a sequence of random variables with probability function: $$P(X_n=1) = P(X_n=2)=P(X_n=4)=P(X_n=5)=0.25$$ and $$Y= \sum_{n=1}^\infty\frac{X_{n}}{5^n}$$ I want to show that: ...