Tagged Questions

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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 $p_1-p_4$.
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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 ...
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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 ...
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$Z$~$N(0,1)$ 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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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.
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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 ...
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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 ...
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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 ...