All Questions
Tagged with expected-value variance
223
questions
2
votes
1
answer
145
views
Expected Value Chi Square distribution
I'm trying to simulate the distribution from the sample variance $s^2$ and compare it with the theoretical distribution.
Therefore, I perform a fairly simple simulation (upfront, I'm not a ...
- 33
0
votes
0
answers
25
views
Expected value of a decreasing function of two random variables
My question is exactly equal to the question posted at Expected value of decreasing function of random variable versus expected value of random variable with just one extra assumption: the two random ...
- 1
0
votes
0
answers
78
views
Derive the expectation and variance of squared sample correlation: delta-method or else?
I would like to obtain the expectation and variance of the squared Pearson sample correlation ($\operatorname{E}(R_{lk}^2)$ and $V(R_{lk}^2)$) between two random variables $l$ and $k$ following a ...
- 215
0
votes
0
answers
21
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Verifying the integrability condition of a deterministic volatility function
Suppose there is integrability condition:
\begin{equation}
\mathbb{E}\left[\int_0^T\frac{\sigma^2(t)}{T-t}dt\right]<\infty
\end{equation}
for an arbitrary volatility function. Suppose I nominate ...
- 1,226
2
votes
1
answer
60
views
Expectation and variance of bivariate skew normal distribution
I am fitting a bivariate skew normal distribution to a 2D data through the sn package in R. I get a $2 \times 1$ vector of ...
- 163
4
votes
1
answer
105
views
Mean Squared Error for point estimation
I am attempting to understand Mean Squared Error when evaluating point estimators for particular parameters of interest. The book we are reading for class states the following:
The mean squared error (...
- 345
1
vote
0
answers
85
views
How to find $\mathbb{E} \left[\frac{\bar{\mu}}{\bar{\sigma}^2}\right]$?
I asked the same question on math stacks: MathStacks:, and some user suggest to ask it here for better insight. So this question has found interest in many research problems, but there have been no ...
- 11
0
votes
0
answers
23
views
Question regarding probability and maximum possible variance
I have the following question:
Suppose we have a set of 10 numbers (1, 2, ... , 10), each with a certain probability tagged to it.
Is it true that the highest possible variance is achieved when 1 and ...
- 31
1
vote
0
answers
42
views
Derive Cramer-Rao lower bound for $Var(\hat{\theta})$ given that $\mathbb{E}[\hat{\theta}U]=1$
I am trying to derive the Cramer-Rao lower bound for $Var(\hat{\theta})$ given that we already know $\mathbb{E}[U]=0$, $Var(U)=I(\theta)$ and $\mathbb{E}[\hat{\theta}U]=1$. I am struggling with using ...
- 11
1
vote
0
answers
24
views
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. ...
- 11
0
votes
0
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39
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Given two rvs $X$ and $Y$, if $X Y = Z$, is it possible to change the mean and sd of $X$ without changing the mean and sd of $Y$ and $Z$
I have two lognormal rvs $X$ and $Y$, and a third rv $Z$ which is the product of the former two. I know the mean and standard deviation of the three.
Is it possible to calculate an alternative pair of ...
- 113
2
votes
3
answers
375
views
Expected value and variance of median
Suppose $Y|\Lambda\sim U(0,\lambda)$ with $\Lambda \sim U(0,1)$. If there is sample with size $n$ of $Y$ (To simplify, assume $n$ is odd, so $n=2m-1$). How do I calculate the expected value of median (...
- 23
0
votes
0
answers
54
views
Variance of powers of a standard normal random variable
To predict growth of money in a stock market I try to calculate expected return over a longer timeframe (e.g. 30 years) with a confidence interval. The simple math of taking an average stock market ...
- 139
2
votes
0
answers
53
views
Count distribution in which the mean is equal to the standard deviation?
I have a data set with counts that exhibit the sample property that
$$\hat \sigma_x \approx \bar x$$
which is to say that the sample standard deviation (with Bessel's correction) appears to ...
- 9,401
1
vote
1
answer
49
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Variance of $X + \alpha^\top Y$ where $X$ is a scalar random variable and $Y$ is a random vector [duplicate]
Consider a scalar random variable $X\in\mathbb{R}$, a vector random variable $Y\in\mathbb{R}^n$ and a constant (non-random) vector $\alpha\in\mathbb{R}^n$. I want to compute
$$
\mathbb{V}[X + \alpha^\...
- 657