# Questions tagged [variance]

The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.

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### mean and variance

Let X be a discrete random variable such that X = 0 with probability 0.5 and X = 1 with probability 0.5. Let Y be a discrete random variable such that Y = 1 when X = 1 and Y = 0 when X = 0. What is ...
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### Why is the variance smaller for the same coefficient in a reduced regression model vs. full regression model?

Let's say we have two estimators for $\beta$. $\beta$ denotes all a full set of coefficients, one for each covariate in a dataframe. $\beta$ can be split into $\beta_p$ and $\beta_r$, where $p$ ...
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### Expectation and Variance of two sets

In genomics, you have an input control (I) and a treatment (T) where then you determine the ratio T/I. You perform multiple replicates for each but the number of replicates is not always the same. ...
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### Variance in set of different random variables

Imagine we have sample of values a_1, a_2,...a_n, with a_i value originating from a normal distribution with mean mu_i_a and variance var_i_a, thus each value is single realization of different random ...
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### Unbiased estimator of $\sigma^4$

In the post [here], the user asked the question $\{X_i\}_1^n$ is random sample from $N(\mu, \sigma^2)$ with unknown parameters. Find an unbiased estimator of $\sigma^4$. The solution uses a property ...
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### Which type of t-test is best to use for my data

I'm looking for some guidance on which type of t-test is most suitable to use for my data. I want to compare the means of the variable 'Rate' between two groups in my data. I have 6 years of data and ...
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### Misunderstanding on the use of Popoviciu and von Szokefalvi Nagy's inequalities on the variance of a unbiased estimator

Let $X_1,\cdots,X_n$ be (discrete in my case) i.i.d. and bounded between $m$ and $M$. I'm interested in bounding the variance of an unbiased estimator: $$\mathbb{V}\left[\frac1n\sum_{i=1}^nX_i\right]$$...
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### How to solve MME [closed]

I have spent an entire day trying to figure out how to solve these mixed model equations without any luck. I am therefore reaching out to this community. The assignment is as follows: Using the ...