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5 questions
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Expected value of X given Y is less than some constant [duplicate]
Here is the problem I'm trying to work out: Let $v_b,v_s$ be jointly normally distributed random variables with pdf $f(v_b,v_s)$. I want to work out $E[v_b|v_s\leq\pi]$ for some constant $\pi$. Here ...
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What is the expected value of half a standard normal distribution?
You have a normal distribution with mean of 0 and variance of 1. Keeping the same probabilities and focusing only on half of the distribution (other half has it's original probabilities but x values ...
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Expectation of the inverse of $\textbf{z} \textbf{z}^{H}$ where $\textbf{z}$ is a complex Gaussian vector
Considering the vector $\textbf{z} \sim \mathcal{CN}(\textbf{0}_{M},\Theta_{M \times M})$, what would be the expectation of $\frac{1}{\textbf{z} \textbf{z}^{H}}$, i.e.,
$\mathbb{E} \left\lbrace \frac{...
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Help to understand this. Expected value of $S^\alpha$ in Gaussian distribution [closed]
Lets $X_1,\cdots,X_n$ be simple random sample from $\mathcal{N}(\mu,\sigma)$.
$\overline{x}$ is sample mean.
Let
$$S^2=\begin{cases}\sum_{i=1}^n (x_i-\mu)^2, \mathrm{ where\ } \mu \mathrm{\ is\ ...
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How to calculate the expected value of a standard normal distribution?
I would like to learn how to calculate the expected value of a continuous random variable. It appears that the expected value is $$E[X] = \int_{-\infty}^{\infty} xf(x)\mathrm{d}x$$ where $f(x)$ is the ...
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