Tagged Questions

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis.

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82 views

Find an unbiased estimator

Let $X$ be an r.v defined by $P(X=0)=p$ and $P(X=1)=1-p$. Find an unbiased estimator for $2p$. My solution: $E(X)=1-p$ so $2-2E(X)$ is unbiased. Is this correct?
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159 views

Expectation by conditioning

Problem: Independent trials, each of which is a success with probability $p$, are performed until there are $k$ consecutive successes. What is the mean number of necessary trials? Start on solution. ...
1answer
105 views

Confidence interval for n=1, unknown standard deviation

Is there any way to calculate a confidence interval (or otherwise gauge the reliability of a sample) when you have a sample size of one and you don't know the population standard deviation? I work at ...
2answers
1k views

Meaning of covariance

Can someone please give me an intuitive explanation for the meaning of covariance between two random variables? What does it measure?!
1answer
2k views

Upper and Lower Bounds for Confidence Intervals on a one tail hypothesis test.

CI(99) = xbar ± Zcv( σ / √ n -1 ) My question is if the test is a one tail hypothesis test, do I still do two separate equations + and -. Here is the formula filled in (if it is the correct formula)...
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Why am I getting 84.25 instead of 97.68 for my Confidence Interval?

Why am I getting 84.25. I am doing 97.96*(6/sqrt[50-1]) = 97.96*(6/7) I am obviously not doing this correctly please help. It has been sometime since I have done any math.
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44 views

statistical significance in non normal distributed data

I have randomized strings undergoing two different tests. There's a pretty clear difference in their proportions, but it reminded me of apstats where you would often do 2prop Z-tests to compare to ...
1answer
83 views

Expected Value of a function of the standard normal distribution

Any help is appreciated. Thanks
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Get overall sum having partial data

I have partial data of online game ingame sales. I know the data for N users. The overall game users count is M which is about 6 times greater than N. I can calculate overall revenue for N users. But ...
2answers
23 views

Binomial probability on ports

This problem appears very simple, but I am almost positive that it should not be so simple. 10 ports. P1,P2,P3...P10 are connected to a computing device which polls them in order to check which ...
1answer
308 views

Probability statements in a true or false format

The following questions are to be answered as preparation to my exam next Friday. I feel I understand the terms, such as "complement", "union", and "intersection", but when confronted with questions ...
1answer
98 views

Normal Distribution - Statistics

True or false statements The central limit theorem implies that any sample of any size can be approximated using normal distribution. Let X be a normal random variable with mean 3 and variance 16. ...
1answer
60 views

How do we square a random variable?

How do we square a random variable? For example, Let $Y=X^2$. $$f_X(x)={\frac{1}{\sqrt{2\pi}}} \cdot e^{\tfrac{-x^2}{2}}$$ How do we derive $f_Y(y)$? Thanks in advance.
1answer
25 views

Test for Validity of Artificial Samples

I have a model that actually is learned from some observed samples. Then I use the model to generate several artificial data. My question is: Which test should I use to test if the data is of the ...
0answers
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Quantitatively comparing event trains of different lengths for Poissonness

I have a parameterized, effectively black box process that generates a series of events (simulated action potentials). Different parameter values often lead to different numbers of events. How can I ...
1answer
64 views

Confidential interval for ratio of mathematical expectations

I've got 2 sequences of Bernoulli random variables: ${X_1, ... , X_n}$ and ${Y_1, ... , Y_n}$ For each mathematical expectations ($EX$ and $EY$) of these sequences i can find confidence intervals. But ...
1answer
26 views

Find alpha when we know valuse of student distribution

Assume, we have $t_{1-\alpha/2,39} = 2.252401$. I don't know how can find $\alpha$. Please help me and how find it in R.
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69 views

What is the corrected sample standard deviation when there is only one sample?

What do we say about the corrected sample standard deviation when the sample size is one? Do we just assume it is 0? Is it even meaningful? The usual equation seems to fall apart here because N - 1 ...
1answer
38 views

Solving for a ridge penalty given a fitted model

This is kind of embarrassing; I once knew this stuff, and I've forgotten it. I've got a fitted ridge regression: $$\hat\beta = \left(X'X+\lambda\right)^{-1}X'y$$ X is n by k y is n by 1 $\lambda$...
1answer
43 views

Help with the birthday probability problem

Say there are lottery tickets with three numbers. Each number has $100$ possibilities. There are $N$ tickets sold where $N > 1000$. I've tried $$\frac{1 − 100!}{(100 − N)! 100^N}$$ ...
2answers
110 views

Returns probability

I have following investment data: mean-8 standard deviation 15 Assume that if it is normal distribution, what is the probability that returns will exceed 23%. How to calculate this?
1answer
581 views

Method of Moments and Maximum Likelihood question

Suppose that $X_1,X_2,…,X_n$ are an i.i.d. random sample from a Rayleigh distribution with parameter $\theta > 0, f(x|\theta) = \frac{x}{\theta^2}e^{-\frac{x^2}{2\theta^2}}, x>=0$ Find the ...
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164 views

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what value for $c$ yields the estimator for $σ^2$ with the smallest mean square error among all estimators of …

If $S'^2 = \dfrac{\sum_{i=1}^n (Y_i - \bar{Y})^2}{n}$ and $S^2 = \dfrac{\sum_{i=1}^n (Y_i - \bar{Y})^2}{n-1}$ then $S^{'2}$ is a biased estimator of $σ^2$, but $S^2$ is an unbiased estimator of the ...
4answers
9k views

Establishing the upper and lower bounds of normal using standard deviation

I understand the concept of standard deviations and z-values, but I'm trying to figure out if standard deviations alone are good for establishing the upper and lower bounds for normal. For example, if ...
0answers
37 views

standard deviation estimation after changing part of data to be constant

If we have a sample of known average and standard deviation, for example, 5 and 1. Suppose that we have a constant for which the CDF is 10%. The values below the constant are set to equal the constant....
1answer
32 views

some misunderstand about student distribution and R

I see on book : $t_{0.025,59}$ = 2.009 But when call qt in R. We have this result: qt(0.025,59) [1] -2.000995 I don't know why have different in here. As I think, $t_{0.025,59}$ must is ...
1answer
261 views

Prove that the usual (1-$\alpha$)% confidence interval for $\sigma^2$ is NOT the shortest interval.

Prove that the usual (1-$\alpha$)% confidence interval for $\sigma^2$ is NOT the shortest interval. In particular, show that the minimum length interval satisfies $f_{(n+3)}(a) = f_{(n+3)}(b)$, where ...
0answers
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If $S'^2 = \frac{\sum_{i=1}^n (Y_i - \bar{Y})^2}{n}$ and $S^2 = \frac{\sum_{i=1}^n (Y_i - \bar{Y})^2}{n-1}$, find $V(S'^2)$.

If $S'^2 = \frac{\sum_{i=1}^n (Y_i - \bar{Y})^2}{n}$ and $S^2 = \frac{\sum_{i=1}^n (Y_i - \bar{Y})^2}{n-1}$ then $S'^2$ is a biased estimator of $σ^2$, but $S^2$ is an unbiased estimator of the same ...
2answers
957 views