Tagged Questions

4
votes
0answers
38 views

How to test whether mean and variance is the same in two small samples?

I would like to test two relatively small samples against the null hypothesis that both their means and variances are the same. The alternative would be that they in fact differ. I saw a post on this ...
1
vote
0answers
49 views

Mean and variance of call center data

I have a fairly involved homework question, I was wondering if I could get some help. There are two types of phone calls arriving at a switch, long-duration and short-duration. Each day the number ...
1
vote
1answer
29 views

Mean and variance of number of tries required

So the question states that I'm trying something with an 85% chance of success, if I don't succeed I try again until I do. What is the mean and variance of the number of tries necessary until I ...
0
votes
2answers
62 views

Simple homework question about normally distributed variables

The question states: Consider a set of random variables $X_i$, where $i=1,...n$. Each $X_i$ is normally distributed with mean $0$ and variance $1$, i.e. $X_i$ are $\mathcal N(0,1)$. What is ...
0
votes
0answers
24 views

Variance of an estimator, as mean of $5$ estimates

Might be a stupid questions, but I realized it is something I haven't encountered until now. So I have 5 estimators for the same quantity, say $X_1,\dots, X_5$, (where each one uses a perturbed data ...
0
votes
1answer
120 views

Show that $E(XY) = σ_{XY} + μ_Xμ_Y$?

Let X and Y be two random variables with means $μ_X$ and $μ_Y$ , variances $σ^2_Y$, $σ^2_X$ and covariance $σ_{XY}$ . Show that $E(XY) = σ_{XY} + μ_Xμ_Y$? I tried the Covariance formula with: ...
0
votes
5answers
184 views

How can I find distribution from mean and variance

If I know the mean and variance of a discrete random variable $\in \{0,1,\dots \}$, How can I find the distribution?
0
votes
0answers
61 views

What is a (rule of thumb) good signal-to-noise ratio?

Is there a rule of thumb for a signal-to-noise ratio that can be considered "good"? In my case, for example, I got a signal-to-noise of 2.5, but in absence of a good benchmark I can't tell if this ...
0
votes
0answers
37 views

Calculate proportion among means with variance and CI

I have two groups of samples, with their own mean, SEM, CI. I would like to calculate the proportion in percentage between the two. Rationing the means is easy but I don't know very well I should I ...
0
votes
0answers
47 views

Compare variability in different groups

I have 3 groups with a distribution of samples. I used ANOVA to compare means of these groups and also fetched mean, SD and SEM. I have SD and SEM that varies among groups. How can I compare them so ...
0
votes
1answer
66 views

How large a variance can be for a discrete random variable whose mean is known?

In following Maximum value of coefficient of variation for bounded data set I come up this question: e.g., Say, $X$ can take integer values from $[0, 20]$ The mean of $X$ is known to be $0.005$ What ...
0
votes
0answers
78 views

Statistical tests affected by the mean values of the two samples

The experiment consisted of this : 31 devices of type $A$ 26 devices of type $B$ All the 57 devices were side by side in order to measure the level of ambiant radiation. So, I have the doses for ...
1
vote
1answer
122 views

Find the mean and variance of $U_1 + U_2$

Let $Y_1, Y_2, Y_3$ be i.i.d continuous random variables. For $i = 1, 2$ define $U_i$ as $U_i=1$ if $Y_{i+1} > Y_i,$ $=0$ ,otherwise Find the mean and variance of $U_1 + U_2$ I can't find the ...
2
votes
1answer
1k views

Kurtosis/4th central moment in terms of mean and variance

Is it possible to express the kurtosis $\kappa$, or the 4th central moment $\mu_4$, of a random variable $X$ in terms of its mean $\mu = E(X)$ and variance $\sigma^2 = Var(X)$ only, without having to ...
1
vote
2answers
570 views

How to assess accuracy of phone GPS in measuring distances?

I am a complete stranger to statistics (apart from mandatory courses in college), but lately I ran into an interesting real-world scenario. Recently I started jogging. I take my GPS phone with me to ...
2
votes
1answer
317 views

How to combine subsets consisting of mean, variance, confidence, and number of sampled points used?

I have a data set that has been divided into $n$ data subsets. I am sampling from each of these subsets and getting a tuple consisting of mean, variance, confidence and number of sampled points used. ...
2
votes
0answers
258 views

R limma voom function mean-variance trend

I am using the limma package in R to do some analysis on a count data matrix. I use the voom function and that normally creates a plot with the mean variance trend line in it. Now I created also a ...
1
vote
0answers
761 views

What does a squared coefficient of variation signify?

The coefficient of variation is defined as the ratio of S.D to mean, a dimensionless number which on multiplication by 100 gives the percentage of dispersion with mean. But when we square this ...
0
votes
0answers
2k views

Can variance be equal to mean?

I came to know that variance can be zero if all data points are equal. Can anybody state an example, where calculated variance is equal to mean and what is its significance in distributions like ...
1
vote
1answer
119 views

How many samples should be taken to capture the mean and variance of the original set with given error?

I have a set $S$ of $N$ real numbers. I wanna calculate the mean $m$ variance $v$ of $S$. But since $N$ is too large, I do not want to use all of the numbers. Instead, I would like to sample $n$ ...
1
vote
0answers
118 views

How do I test whether differences in populations are significant?

I'm working on a large database. I want to explore whether certain batch jobs run in more or less time after a change was than they did before the change. There are about 90 distinct batch jobs. They ...
0
votes
1answer
183 views

Deriving ${\rm var}(\overline{X})$ from expected value definition

I want to show ${\rm var}(\overline{X})$ is $\sigma^2/ n$ for $n$ independent random variables each with mean $\mu$ and standard deviation $\sigma$. I would like to show this using: $$ ...
2
votes
2answers
828 views

How to compare the variance of two conditions with different means?

I have a series of vectors, which are measurements from one sample at two time points. First time point: 1.[5,3,2,4,4,3,6,5] (mean=4.000) 2....
5
votes
2answers
235 views

One component in PCA is always the mean vector in two-dimensions but not three

I've been testing PCA via SVD to decompose a simple time series data matrix, $X$. I have two signals $x_1(t)$ and $x_2(t)$ in a data matrix where $M$ rows represents each timepoint sample and each ...
3
votes
2answers
398 views

Calculating sample mean and sample variance on all samples vs distinct subsets

Consider 1000 samples drawn from an unknown distribution. Whats the difference between the following two ways of calculating sample mean and sample variance? find sample mean and sample variance ...
9
votes
2answers
1k views

Maximum value of coefficient of variation for bounded data set

In the discussion following a recent question about whether the standard deviation can exceed the mean, one question was raised briefly but never fully answered. So I am asking it here. Consider a ...
3
votes
1answer
1k views

Comparing standard deviations between variables with very different ranges

I have a number of variables for which I want to compare the standard deviations. Each of these variables is actually the data for a particular wavelength of light, and I want to produce a plot ...
1
vote
1answer
161 views

Slope and intercept of linear equation of uniformly distributed variables

Consider the random variable $y_M$ which equals the sum of $M$ independently uniformly distributed random variables; i.e., $y_M = x_1 + x_2 +\ldots + x_M$, with the assumption that each of the $x_i$ ...
0
votes
1answer
242 views

Mean and variance of a normally distributed random number created from the average of a set of uniformly distributed random numbers

An old-fashioned way of generating normally distributed random numbers entailed setting each normally distributed random number equal to the average of a set of uniformly distributed random numbers, ...
0
votes
1answer
337 views

How to do 'normalization'?

How do you do normalization so that when I get the mean/variance, the flat values wont affect the results? For example, in the figure below, Graph 1 & 2 are both considered to be noisy as compared ...
4
votes
2answers
2k views

How to intuitively understand formula for estimate of pooled variance when testing differences between group means?

Suppose I want to compare the difference between means of samples selected from two populations (the treatment and control). Assume both groups have normally distributed observations. Then $$Z = ...
2
votes
1answer
64 views

Computing descriptives statistics for sites and locations based on literature search with sites having varying numbers of time points

I've collected a data set from the literature. These data are largely binomial: they are clutch sizes of a bird that lays only 1 or 2 eggs in most areas, and in some areas will lay 3. However the only ...
7
votes
2answers
297 views

How can I test $H_0:\sigma^2_1=\sigma^2_2$?

I have a few hundred estimates of a parameter calculated from two different models and I would like to know if these parameters have different variances. What is a straightforward test for comparing ...
4
votes
2answers
98 views

Distribution of a random segment on a string

I have a linear string of unit length, and I randomly sample two locations a and b from Uniform(0, 1). Then I cut the string at these two locations to get a sub-string. What is the distribution for ...