All Questions
Tagged with expected-value mean
84
questions
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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
11
votes
1
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992
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Expected number of correct answers to exam if I guess at each question
I do an exam with $12$ questions. There are $5$ possible answers to each of the $12$ questions.
Is this the expected number of correct answers if I guess answer for each question? $$\frac15 \times 12 ...
- 14.5k
1
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1
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193
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Finding the expected value for the mean squared
The question I tried to solve, but failed, goes like this:
Find the expected value of $(\bar{X}_n)^2$ and find an ubiased estimator for $\mu^2$.
This is the solution given by the TA:
$$E[(\frac{1}{n}\...
- 699
1
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2
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285
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Variance of the difference of two iid sample means
Let $X_{1}, ..., X_{n}$ be random variables independent of $Y_{1}, ..., Y_{n}$, where both groups are iid with associated population means $\mu_{1}$ and $\mu_{2}$ and population variances $\sigma_{1}^{...
- 13
1
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1
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441
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How do we relate RMS and standard deviation for continuous signals?
Because the discrete formula for RMS, $\displaystyle X_{RMS}=\sqrt{{1 \over N}(x[1]^2+x[2]^2+...+x[N]^2)}$, is almost the same as the formula for standard deviation (assuming mean zero), except for a ...
- 209
2
votes
1
answer
209
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In statistics how does one find the mean of a function w.r.t the uniform probability measure?
I am unfamiliar in statistics. My knowledge is in pure mathematics.
Suppose $n\in\mathbb{N}$, where $X$ is in the $\sigma$-algebra of Caratheodory-measurable sets such that $X\subseteq\mathbb{R}^{n}$ ...
- 161
2
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1
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When would the variance for a probability distribution give the same result as the standard equation?
Variance equation for a probability distribution:
$$
\sigma^2 = \sum_{i=1}^{N}(x_i-\mu)^2P(X=x_i)
$$
Standard variance equation:
$$
\sigma^2 = \frac{1}{N}\sum_{i=1}^{N}(x_i-\mu)^2
$$
I understand that ...
- 123
7
votes
3
answers
1k
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When to use Mean(X/Y) versus Mean(X)/Mean(Y)?
So, I understand that for two vectors of numbers X and Y the mean of X/Y is different from the mean of X divided by the mean of Y. But I'm not sure when it is appropriate to use each. Specifically, I ...
- 73
1
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Interpretation problems of linear model with no predictors
Let $Y=X\beta$, where $X=(\begin{matrix}1 & 1 & 1\end{matrix})^T$, $Y=(\begin{matrix}6 & 5 & 4\end{matrix})^T$ and $\beta=(\begin{matrix}\beta_0 \end{matrix})$. Now $X\beta=(\begin{...
- 145
2
votes
1
answer
634
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Expectation of a random variable with positive density at infinity?
Let $X$ be a continuous random variable with pdf $f(x)$. Assume that
$f(x) \geq 0$, for all $x > 0$, so $X$ is a positive random variable,
$f(\infty) > 0$, i.e. $X$ has a strictly positive ...
- 51
1
vote
1
answer
186
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conditional quantile and conditional expectation
I was reading some papers and I found some parts are tricky to understand.
Assume I have price data , what does it mean to calculate the conditional mean of the price data given yesterday price ? ...
- 61
1
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0
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183
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Calculate the mean and the variance of the Kappa statistic
The Kappa statistic was defined as following:
$\kappa = \displaystyle\frac{p_o-p_e}{1-p_e}$, where $ p_o = \displaystyle\sum_{i=1}^{k} p_{ii}$ is the observed agreement, and $p_c = \displaystyle\sum_{...
- 111
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2
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929
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Average count of overlap between random samples
If I randomly sample n numbers from 1..m, x times, what would be the average count of ...
- 13
2
votes
1
answer
55
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Why is the expected value of any data point in the sample equal to population mean?
Suppose we have a distribution of heights of all males in a country.
Let population size = N.
Now, I take a sample of 100 males = {h1,h2,h3,....h100}
How is the expected value of any data point, i.e., ...
2
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On average what is the norm of a sample from a multivariate normal distribution? [duplicate]
Problem
Suppose I sample a multivariate standard normal sample $x \sim N(0, I_d)$ where $d \geq 1$ is the dimension. What is the expected value of the norm of $x$
$$
\mathbb{E}[\|x\|] = ?
$$
Using ...
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