Tagged Questions

3
votes
1answer
40 views

Expected number of duplicates (triplicates etc) when drawing with replacement

I have the following problem: I have 100 unique items (n), and I'm selecting 43 (m) of them one at a time (with replacement). I need to solve for the expected number of uniques (only selected once, ...
2
votes
3answers
91 views

Probability $X$ is less than mean

Let $X$ be a random variable with expected value $\mu$. I need an upper bound on $\Pr( X < \mu )$. All of the bounds I could find deal with something like $\Pr( X < \mu - a)$ and become ...
0
votes
0answers
47 views

the expected value of your gain

You flip a coin and if it is a head I pay you 1 pound but if it is a tail you pay me 2 pounds. You have 50 pounds and you stop when you spend all of your money or you flipped coin 100 times. What is ...
3
votes
1answer
146 views

Expectation and confidence intervals of a Poisson process

A Poisson process has PDF $$P(X=k)=\frac{e^{-\lambda t}(\lambda t)^k}{k!}$$ I'm trying to find an expression for: $E[X | \lambda, t]$ Confidence intervals (i.e. find $\delta$ such that ...
2
votes
0answers
117 views

Name for $E[X]^2/E[X^2]$?

Has anyone seen the following quantity come up in the literature? $$\frac{\mathbb{E}[X]^2}{\mathbb{E}[X^2]}$$ I saw it in equation 10 of this paper.
0
votes
0answers
88 views

How to express the expected value of revenue w/ reserve price in 2nd price auction?

Breifly speaking, the problem comes from setting a reserve price in 2nd price auction, where w/o a reserve price $a_t$, the winner pays the 2nd highest bid $b_t$. But w/ a reserve price, the winner ...
1
vote
1answer
54 views

Finding variance?

$\newcommand{\Var}{\mathrm{Var}}$ Consider $Z_i$ as a binary random variable with $\mathrm{Pr}[Z_i = 1] = \pi$. Also, consider $Y_i$ as: $Y_i|Z_i = 0 \sim \mathrm{Poisson} (\lambda_0) $ $Y_i|Z_i = 1 ...
2
votes
1answer
105 views

“Running it” multiple times in No-Limit Hold'em poker

Suppose on the flop in no limit hold'em two players go all-in. They both have 2 hole cards and there's 3 community cards on the board at present. There will be 2 more cards drawn and each player will ...
11
votes
4answers
541 views

Why is statistics useful when many things that matter are one shot things?

I don't know if it's just me, but I am very skeptical of statistics in general. I can understand it in dice games, poker games, etc. Very small, simple, mostly self-contained repeated games are ...
3
votes
1answer
121 views

Find probability and expectation

18 boys and 2 girls are made to stand in a line in a random order.Let $X$ be the number of boys standing in between the girls .Find $P[X=5]$ and $E[X]$. I proceed in this way: Note that ...
0
votes
0answers
68 views

Building a betting tip system based on previous matches

I'm a newbie so I have only basic statistical skills. I'm wondering if it is possible to use any stat test to analyze the previous matches between 2 tennis players to build a solid betting tip that ...
5
votes
1answer
142 views

Expected value for discrete (nominal) variable?

I'm trying to understand the concept of the expected value. Especially, what bothers me is the expected value for discrete random variables. I will try to formulate it by examples: The expected ...
2
votes
2answers
168 views

$E(\min_{1 \leq i \leq m} |x - y_i|)$

I have faced a statistical problem in a computational biology question. I will explain it in statistical language. Let's say we have the results of rolling one red die, $x$, and $m$ black dice ...
0
votes
1answer
152 views

Expected value of min X for bernoulli success?

I take a SRS sample of size n from a population of x values ranging from 1 to N. Each selected unit also has a probability p of success or q = 1-p of failure (i.e. the probability of success/failure ...
9
votes
3answers
335 views

Expected number of unseen cards when drawing $2n$ cards from a deck of size $n$

We have a deck of $n$ cards. We draw cards from it uniformly at random with replacement. After $2n$ draws what is the expected number of cards never chosen? This question is part 2 of problem 2.12 in ...
1
vote
3answers
740 views

Expected value of the reciprocal of a random variable

Given that $X$ is random variable that takes values: $0,\dots,H-1$ The PMF of $X$ is unknown, but I can tell what is the expected value which is $\bar{X}$ There is event $Y$ when calculated it ...
0
votes
1answer
141 views

Simulating continuous distribution using discrete distribution

I have a continuous random variable $X$ (positive). I want to simulate its distribution with a discrete distribution and calculate $E[X]$ from that discrete distribution. So, the obvious approach is ...
1
vote
1answer
516 views

How to solve Chuck-a-Luck puzzle

Story (spoilers!) The puzzle: Chuck-a-Luck is a gambling game often played at carnivals and gambling houses. A player may bet on any one of the numbers 1,2,3,4,5,6. Three dice are rolled. ...
0
votes
3answers
156 views

Expected value of a random variable in a range

I have a random variable $x$ with $E(x) = \mu$ and PDF $f(x)$ and CDF of $F(x)$. Is there any way to represent the $E(x|x<\bar{x})$ in terms of $\mu$ and $f(x)$ or $F(x)$? i.e. to write the ...
0
votes
1answer
167 views

Expected value of non-standard quadratic form

Say I have two $n$-vectors $f(t)=(f_1(t), \dots, f_n(t))$ and $f(s)=(f_1(s), \dots, f_n(s))$, both with expected value 0. Let $\operatorname{Cov}(f(t)) = a \Sigma$ and $\operatorname{Cov}(f(s)) = b ...
3
votes
1answer
188 views

Meaning of this expectation equation?

I was actually looking at this problem on slide 12. I will write it here briefly: Problem: Unknown number of people arriving in a fixed time period and my goal is to maximize my probability of ...
3
votes
2answers
2k views

Expected value of certain exponential transformation of standard normal variable

This is in reference to the Girsanov theorem however question is general. If $X$ is a standard normal variable $N(0,1)$, why is expectation of $e^{-\mu X - \mu^2/2}$ equal to 1? Shouldn't it be ...
5
votes
3answers
218 views

Increasing Exam Expected Mark

You are in an exam, and are presented with the following question: Write down what mark do you expect to take in this exam... If you get it right in range of +/-10 % then you will take 10% ...