How 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...
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 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...
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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 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...
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 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 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 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 $$...
View ArticleThe expected value of a bunch of dependent events
Suppose we have $2n$ numbers randomly selected in $[0,1]$. $$ (a_1, b_1) rightarrow (a_2, b_2) rightarrow … (a_n, b_n) $$ Suppose we loop from 1 to $n$ and at each step $m$ we choose one of $a_m$ or...
View ArticleExpectation of squared sample t statistics
Given i.i.d data points $X_{1},…,X_{n}$ from unknown smooth distribution $f(x)$ with $EX=theta$ with parameter dimension 1. Let $bar{X}=sum_{i=1}^{n}X_{i}/n$, and...
View ArticleExpectations of kernel density estimate
Suppose $X_{1},…, X_{n}$ are independent and identically distributed according to the probability density function $f$. Let $${hat{f}}_hleft(xright)=frac{1}{nh}sum_{i=1}^nKleft(frac{x-X_i}{h}right)$$...
View ArticleHow to derive conditional expection for a linear combination of independent...
Suppose we have the simple set up $Y = alpha X + epsilon$ Where $X$ and $epsilon$ are both mean zero, variance one and independent. $alpha$ is a constant. Trivially, $E[Y|X] = alpha X$. By simple...
View Article$f(x)$ is an increasing function. $langle X_1 rangle > langle X_2 rangle...
Let $f(x)$ be an increasing function. Consider two random variables $X_1$ and $X_2$, with different probability distributions, such that $langle X_1 rangle > langle X_2 rangle$. Does it follow that...
View ArticleExpected Value of a transformation of a random variable
Suppose there is a random variable $X$ which is defined as follows:$$X=ktimes log(Y)$$ where Y is distributed uniformly on the $[0,1]$ interval and $k$ is a negative real number. I want to calculate...
View ArticleExpected value of multiplication of elements in a normal vector
Suppose we distributed vector $X=[x_1,...,x_N]$ from $N(0,Sigma)$, in which $Sigma in R^{Ntimes N}$ Now how can I compute $E[x_ix_j]$? How can I compute $E[x_i^2 x_j x_s]?$ ($i,j,sin [1,N]$)
View ArticleHow to properly project a value representing 38% to 100% to show potential...
I have a value that represent 38% of user market data, I want to expand the 38% to 100% but doing so may very well be inaccurate because the 38% user behavior may be different than the rest of users....
View ArticleDummy coding: code two values $a$ & $b$ instead of $0$ & $1$?
I know there are a lot of questions and answers related to dummy coding. But I still wonder if it matters to code a dichotomous variable d in this regression model $$y = beta_1 + beta_2 cdot d +...
View ArticleExpected value of sum of cards
If each card on a regular 52 deck card has points that corresponds to their number (like 2 of hearts is 2 points, 7 of clubs is 7 points), the Jack, Queen, King each being 10 points and you keep...
View ArticleRelation between expectations of two random variables
I have two random variable X and Y. I know that $$E_Xleft[X log frac{X}{e}right] < E_Yleft[Y log frac{Y}{e}right]$$ Using the above relation can I say anything about the relation between $E_X[X]$...
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