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Prove that the following function of binary random variables is monotonic

Consider a binary random variable $y$ over the space $\mathcal{Y} = \{+1, -1\}$ such that $\Pr(y = 1) = q$. Consider also $r$ binary random variables $y^1, \ldots, y^1$ over the space $\mathcal{Y}$ ...
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Normal distribution with absolute value

I am new to the normal distribution topic. While I have understood and solved various different kind of questions, the normal distribution questions with absolute value, are the ones I have no idea ...
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Prove the monotonicity of the expectation of a binary random variable function

Consider $R$ independent binary random variables $y^1, \ldots, y^R$ over the space $\{-1, +1\}$ such that $\Pr(y^j = 1) = p^j \geq 0.5$ and $\Pr(y^j = -1) = 1 - p^j$, $\forall j = 1,\ldots,R$. ...
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I don't know how to calculate this cdf, the modulus is very annoying, because the cdf definition is $P(X< x)$ in my case $P(\omega < x)$. But in the modulus equality I get this $P(-\omega < ... 2answers 337 views Expectation Values inside absolute value operator first: are these equality true ? $$|E[Y]-E[X]|=|E[Y]|-|E[X]|.$$ $$|E[Y]-E[X]|^2=|E[Y]|^2-|E[X]|^2$$ second: what is result of this relation: $$\sum_{i=1}^{3}p_i.(X_i-\mu)^2=?$$ where the$\mu ...
I have the following joint pdf: $f(x,y)=0.5$ where $0 \leq|x|\leq|y|$, $0 \leq|y|\leq1$, and $0$ otherwise The question is: are $X$ and $Y$ independent and uncorrelated? I know that if ...