The expected value of a bunch of dependent events
Suppose we have $2n$ numbers randomly selected in $[0,1]$. $$ (a_1, b_1) rightarrow (a_2, b_2) rightarrow … (a_n, b_n) $$ Suppose we loop from 1 to $n$ and at each step $m$ we choose one of $a_m$ or...
View ArticleExpectation from conditional expectations
Consider a real-valued random variable $X$ and a dichotomus random variable $Ysim Be(p)$, all defined on the same probability space $(Omega, mathcal{F}, mathbb{P})$. Could you help me to show that $$...
View ArticleWhat is the expectation for a multivariate normal distribution?
Assuming we have a multivariate normal distribution Y∼N(μ,Σ) with known μ,Σ, then, how to compute the expectation for this multivariate gaussian, is that exactly equals to μ? Thanks.
View ArticleProbability / Variance [on hold]
A man, in search of a wife, tries two approaches: generous and cheapskate. When the man tries the generous approach, he ends up spending $1000 on his date, who will, eventually, with probability 0.95...
View ArticleExpectation of discrete random variable
Give a sequence of random variables $x_1,..,x_n$ with $x_n$ having a density of: $$f_N(x) = begin{cases} frac{2N-1}{3N};x=1\ 1/3;x=1+frac{1}{N+1} \ frac{1}{3N};x=2end{cases}$$ What would be the...
View ArticleExpectation of t distribution
Find $E(T^{2r})$ of Student’s t-distribution. My teacher has told me the answer…. it’s something like $$ frac{n^r Gamma(r+(1/2)) Gamma(n/2-r)}{Gamma(1/2) Gamma(n/2)} $$ From this I calculated the 2nd...
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Properties of the Residuals of a Binary Logit Model with an Intercept
Hi, So for this problem I thought of taking the log of the residuals to get: $$ Log(e_{i}) = log(D_{i}) – x_{i}gamma_{hat} + ln(1) + x_{i}gamma_{hat}$$ $$ Log(e_{i}) = log(D_{i})$$ Then taking...
View ArticleIs frequentist statistics concerned with expectation? [closed]
Frequentist statistics sees probability as the expectation of the value. Expectation is the long-term average. Do Frequentists interpret probability as the expected value for that parameter? EDIT: From...
View ArticleELO rating for non-pairing sport + serious math
I was considering sport disciplines for which there are multiple players at the event but rather than playing against each other, they do stuff, are assigned points and their final position is based on...
View ArticleHow do I find the expected value of F(isher)-distribution
$E(F)=int xf_{k,m}dx$ where $f_{k,m}(t) = Gamma(t)=frac{Gamma((k+m)/2)}{Gamma (k/2)Gamma(m/2)}k^{k/2}m^{m/2}t^{k/2 – 1}(m+kt)^{-(k+m)/2}$. How do you find $E(F)$? Say you have to convert $x*f(k,m)$ to...
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