Expectation of stochastic integral when integrand is a product of...
I am currently working on BSDEs and looking at some stability results. At a certain moment I need to...
View ArticleExpectation when a partial range is known
Let $X$ be a continuous random variable with a density $f_X(x)$ and let $A\subseteq \mathbb{R}$. Would it be true to claim that:$E[X | X\in A] = \int_{x\in A} x \cdot f_X(x) \cdot dx$?My understanding...
View ArticleExpected Value of Number of Instances of particular sequence
I am trying to answer the question - You toss a fair coin $n$ times. What is the expected number of strings of $h$ consecutive heads assuming overlapping instances are not allowed?In the standard...
View ArticleExpected Number of Coin Flips to obtain sequence HTH
I was working on problems on expectation and was unable to solve this one using generating functionsAssume that you are flipping a fair coin, i.e. probability of heads or tails is equal. Then the...
View ArticleExpected Arrival Time of Busses [closed]
I'm looking at a classic probability question that I'm unable to answer: Assume green buses arrive with U[0, 10] and red buses arrive with U[0, 15]. If you arrive at bus station randomly, what is your...
View ArticleWhat is the expected number of random moves to solve a jigsaw puzzle?
Let's say we're trying to solve a jigsaw puzzle of $N$ pieces, but we're using "brute force". Our strategy is as follows: we pick a spot and then keep trying puzzle pieces until we hit the one that...
View ArticleBounding expected spectral norm of shifted Grammian of a Rademacher random...
Let $S \in {\Bbb R}^{k \times n}$ be a random matrix with independent entries$$ {\Bbb P} \left[ S_{ij} = \pm \frac{1}{\sqrt{k}} \right] = \frac12 $$I am interested in finding the tightest possible...
View ArticleCorrect expression of the loss function for a Negative Binomial distribution
ContextI am trying to obtain an expression for the loss function or expected "shortfall" when lead time demand is a discrete random variable that follows a Negative Binomial distribution. The context...
View ArticleCalculating the expected value and variance of sum of iid normally...
Let $X_1, X_2, ..., X_n$ be an iid sample from $N(\mu, \theta)$, where $\mu$ is unknown. I'm trying to find the expected value and variance of the random variable $Y = \frac{1}{n} \sum_{i=1}^n (X_i -...
View ArticleCan $E(X)$ be defined using the Law of Large Numbers as "universal property"?
As an algebraist who occasionally teaches introductory statistics and probability, this question has been on my mind for a while:Can one use the Law of Large Numbers (LLN) to define the expectedvalue...
View ArticleIntuition for Dice Roll Expected Value problem
I'm studying a chapter on Expected Value right now, and there is an interesting formula here: Imagine a Bernoulli event where there a “success” (such as tossing a coin / rolling a 5 on a dice) occurs...
View ArticleExpected number of Pareto-optimal points
Suppose $S$ is a set of $n$ points in a plane.A point is called maximal (or Pareto-optimal) if no other point in $S$ is both above and to the right of that point.If each point in $S$ is chosen...
View ArticleExpected number of Pareto-optimal points for $d$-dimensional points
I was wondering if it is possible to generalize any of the solutions previous question for the 2-dimensional case to derive the size of the set of the Pareto optimal points for an arbitrary dimension...
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how does huber compute the $var(s_n)/E[s_n]$ and $var(d_n)/E[d_n]$?
How does Huber in book 'Robust statistical procedures' in chapter 1 compute the variance of certain statistical functions?He defines the mean square deviation to be $$s_n = \sqrt{\frac{1}{n} \sum...
View ArticleExpected number of correct guesses when identifying 5 people, blindfolded
The Game: You are blindfolded in front of a line of 5 people. Your task is to identify the ordering of the people in the line.Conditions of the Game:You know the five names of the people, but do not...
View Article$\mathbb E[X\mid Y]=Y$ and $\mathbb E[Y\mid X]=X$ implies $X=Y$
I'm sure this must've been asked before here but I couldn't find it. I'm trying exercise 11.9 from Le Gall's "Measure theory, Probability, and Stochastic processes". The objective is to prove what I...
View ArticleTurducken Hunt OR Optimal Shooting Strategy — Probability Problem with Moving...
Mordecai and Rigby are chasing down the Turkaden. Both starting at x=0, the Turducken 1 meter away. They start walking at the same rate towards x=1. Both only have one bullet in their guns and they can...
View ArticleMaximum of $E[|X+Z|^m]$ for $Z$ standard normal and $X$ independent of $Z$,...
Let $Z$ be a standard normal distribution. I am trying to find a solution to the following problem:\begin{align}&\max_{ x_1,x_2 \in \mathbb{R}, t\in[0,1]} (1-t) E[|x_1+Z|^m]+t...
View ArticleCards Shuffling
Imagine you possess20 cards, each numbered from1 to10, with each number appearing twice. You randomly select2 cards from the20 available cards. If they are identical in value, they are removed from the...
View ArticleDefining Random Variable, Expected Value for Number of Fixed Points given a...
Let $n \in \mathbb N$, and $\mathcal{K}$ be the set of permutations possible for a set $\{1,...,n\}$. Let $\sigma \in \mathcal{K}, $ such that $\sigma: [n] \to [n]$ is a randomly selected permutation....
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