# Tagged Questions

The expected value of a random variable is a weighted average of all possible values a random variable can take on, with the weights equal to the probability of taking on that value.

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### Implicit estimator, it's variance and expectaion

Denote with $V_j$ the firm's value of $j$-th firm. We will speak of default, if the firm's value falls below predefined barrier $c \in \mathbb{R}$. The random variable $L_j$ will indicate, if $j$-th ...
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I am going to use default data, where $d(t)$ stands for amount of defaults in period $t$ and $t \in \{1,\ldots , s\}$; $n(t)$ is total number of credits. Suppose the following equation holds $$... 1answer 319 views ### Expected Value and Most Likely Outcome I was watching this Khan video on Expected Value as a refresher. He mentions in passing that the expected value is the most likely outcome... Well, that's only true because he's using a ... 2answers 31 views ### exact value runtime for coin flip algorithm So I have an algorithm like this: inc = 10 for num in Array: if num == 1: return inc else: inc += 1 inc += 1 return inc I want to ... 1answer 63 views ### On some manipulations of E[( X - tY)^2 ] I am following some notes and don't fully understand a step: call 0 \le f(t) = E[ (X- tY)^2]  then by linearity of the expected value we get$$f(t) =E[Y^2]t^2 - 2 E[XY]t + E[X^2]$$As noted this ... 1answer 40 views ### Which distribution has an expected product equal to one? Consider n values x_{1} to x_{n} such that x_{1}x_{2}\cdots x_{n} = 1. Importantly, these values are non-independent, as their product must be equal to 1. The trivial case of x_{i}=1 \quad \... 2answers 791 views ### Correlation between sine and cosine Suppose X is uniformly distributed on [0, 2\pi]. Let Y = \sin X and Z = \cos X. Show that the correlation between Y and Z is zero. It seems I would need to know the standard deviation ... 0answers 32 views ### Expected value question [duplicate] Say I am rolling a 20-sided die. What is the expected number of rolls to have rolled each number? I haven't taken statistics in a while so my syntax might be off but this question has been bugging me ... 1answer 25 views ### Expectations of cosine under von Mises distribution I'm trying to work out the expectations of a few functions under the von Mises distribution:  p(\theta \mid \mu, \kappa) = \frac{1}{2\pi I_0(\kappa)} \exp\left\{ \kappa \cos \left( \theta - \mu \... 3answers 73 views ### The meaning of expected value for discrete random variable in dice experiments Does the expected value always speak to a payoff? Or can the expected value be thought of independent of payoffs? I don't understand when we say a fair die has an expected value of 3.5. Does that ... 2answers 79 views ### Truthfulness of statements on the expected values of random variables Are these statements true or false? Why? E(|X|)\le 1 + E(X^2) 0≤|x|<1+x^2 for all choices of x with x real number. What with X random variable? if E(X)<0 and  \theta \neq0 ... 2answers 704 views ### Monte Carlo method cannot be used This is an example from notes I don't understand why we should think about the E(x) and Var(x) first? 0answers 9 views ### computing a marginal I have tried to solve this exercise Let X and Y be random variables with joint probability density function given by: f(x,y)=\frac{1}{8}(x^2-y^2)e^{-x} if x>0 ,|y|<x Calculate E(X|Y=... 2answers 136 views ### Expectation of \frac{X_1^4}{(X_1^2 + \cdots + X_d^2)^2} Let X_1, X_2, \cdots, X_d \sim \mathcal{N}(0, 1) and be independent. What is the expectation of \frac{X_1^4}{(X_1^2 + \cdots + X_d^2)^2}? It is easy to find \mathbb{E}(\frac{X_1^2}{X_1^2 +... 0answers 16 views ### Difference between two methods of random point generation [migrated] In order to do a monte carlo simulation to estimate expected distance between two random points in n dimensional space I discovered the following two similar looking methods to generate random ... 1answer 68 views ### Expectation of a function of a random variable from CDF Is it possible to calculate the expectation of a function of a random variable with only the the r.v.'s CDF? Say I have a function g(x) that has the property \int_{-\infty}^{\infty}g(x)dx \leq \... 0answers 10 views ### Expectation of Maximum of Transformed iid RVs Is the following reasoning correct? Let \mathbb{P}(c \leq l) = F_c(l) be the CDF of random variable c and \pi(c) a strictly decreasing positive and bounded function where both are continuous ... 0answers 35 views ### Expectation Value of Standard Deviation from “k” Closest Samples The question that I'm am trying to answer is how to determine the expectation value of the standard deviation of 'k' closest samples to value 'A'. The standard deviation and mean of the underlying ... 1answer 81 views ### Is it okay to write the square of expectation of a random variable X as \mathbb{E}^2(X)? Is this notation accepted when I write \text{Var}(X)=\mathbb{E}(X^2)-\mathbb{E}^2(X)? 0answers 12 views ### Expected value of a semi-partial correlation Say I have 4 random variables. X^{(1)} and X^{(2)} are jointly multivariate normal with mean 0 and covariance \Sigma_X, and Y^{(1)} and Y^{(2)} are jointly multivariate normal with mean 0 ... 2answers 98 views ### Working with percentages of positive variables Say we run an experiment and observe the following impact on a variable of interest (one row per experimental unit): ... 0answers 21 views ### Expectation of infinite sum of random wishart matrices I have problem figuring out how to find the expectation for an infinite sum of random matrices. More explicitly, my problem is: Let \mathbf{S}_i be the maximum likelihood estimator of the sample ... 1answer 35 views ### Expected Value clarifications using R/Excel So it has been a little while since I've taken my last statistics course, and I wanted to double check that I am not making any kind of grave errors in my expected value calculations. Quick bit of ... 2answers 31 views ### Expected number of points in k turns? I'm not too familiar with expected values so I'm wondering if people could verify if I'm on the right track with my thought process here. If the probability of winning one point in a turn is 1/9, ... 2answers 34 views ### Minimising MSE of \sigma^2 estimator of specific form I have found a past exam question for a statistics course and can't seem to find the required result. Part A is fine but my working for part B must be incorrect [see below]. Can anyone figure out ... 1answer 45 views ### How would you calculate E[\mid x \mid ^{\alpha }], \alpha \in \Re? Here x \sim N(0,1). I realize that the expectation won't be defined for \alpha when the integral goes to infinity. I can't seem to figure out which specific values of \alpha would cause this. ... 1answer 49 views ### Finding the expected value of a continuous random varibale when the commulative distribution is given I have this distribution function of a random variable X: I wish to find E(X). I have used derivatives to get the density function, compared it to 1, and found that f(t) = (4/5)t+(3/5). I then ... 1answer 42 views ### Conditional expectation of a univariate Gaussian Suppose I have a univariate Gaussian distribution with mean \mu_X and standard deviation \sigma_X, and I know the random variable X is least some positive value y: X \geq y. What is the ... 1answer 74 views ### How to find E|X+Y|^3 from related information? Assume that$$ E(X+Y)=E(X-Y)=0  V(X+Y)=3  V(X-Y)=1 $$Show that E|X+Y|\leq\sqrt3. If in addition, it is given that (X,Y) is bivariate normal, calculate E|X+Y|^3. For the 1st part, ... 1answer 64 views ### Expectation with indicator function I have the following expectation$$E[x_{t+1} \mathbf{1}_{\{x_{t+1}> z_t\}}]where x_{t+1} is a normally distributed random variable x_{t+1}\sim N(0,\sigma^2), and \mathbf{1} stands for ... 1answer 96 views ### Expected value of maximum ratio of n iid normal variables Suppose X_1,...,X_n are iid from N(\mu,\sigma^2) and let X_{(i)} denote the i'th smallest element from X_1,...,X_n. How would one be able to upper bound the expected maximum of the ratio ... 0answers 38 views ### Expectation of a hazard rate I need to estimate the expectation of a hazard function, E[h(x)]. For instance, for the exponential distribution the result is equal \lambda E[h(x)]=\int_0^\infty \! h(x)f(x)\mathrm{d}x=\... 1answer 46 views ### Expected value word problem from Khan Academy Hello all and thanks for taking the time to read this. I'm closing out the last few sections of statistics in Khan Academy, but there is a problem that is really bugging me. The problem reads like ... 1answer 51 views ### Expected value of difference of two order statistics X_1,X_2,..,X_n is a random sample from the random variable whose pdf is, \begin{align*} f(x)=\lambda e^{-\lambda(x-\mu)},\mu<x<\infty \end{align*} How can we find E(X_{(2)}-X_{(1)}), if n=2?... 0answers 38 views ### How do we obtain E(exp(C+By-Y'aY))? How can I prove this ? I did get B-2uA by identifying the a+by+cy^2= -1/2 (y-u)^2/\sigma^2 But, I don't know how to get (2a+\Sigma^{-1})^{-1} \dots Am I missing something? A little help would ... 1answer 24 views ### Expected value of a function of a multinomially distributed random variable I have a scalar function, g(x), where x is an n-vector following a multinomial distribution with mass f(x;p, N), for some probability-vector p, such that \sum p_i=1 and where \sum x_i = N... 1answer 90 views ### What is the minimum sample size for kaplan meier I used the "survival" package in R to calculate a Kaplan Meier estimate for survival. An example of my output is like this: ... 1answer 78 views ### Approximate Order Statistics for lognormal variables Are there any known formulas that approximate the expected value of the maximum of N i.i.d. lognormal random variables? I am looking for something similar to: Approximate order statistics for ... 1answer 24 views ### expectation of conditional expectation Given (X,Y), 2-dimensional probability vector, and let g: R^2 \rightarrow R, E[g(X,Y)^2 ] < \infty and h:R \rightarrow R, E[h(X)^2] < \infty , prove the following:E[h(X)\{g(X,Y)-E[g(X,...
The expected value of the simple linear regression model $y = \beta_0 + \beta_1x + \epsilon$ is typically written as $E(y|x) = \beta_0 + \beta_1x$. Why is it written as $E(y|x)$ instead of just $E(y)$?...