Expected value Definition and 250 Threads

This question comes from the "Introduction to Probability" book (Blitzstein & Hwang). Martin has just heard about a gambling strategy: bet 1 dollar that a fair coin will land heads. If it does, stop. If it lands tails, then double the bet for the next toss, now betting 2 dollars on heads. If it...

Hello all Currently struggle with a question from one of my assignments concerning poisons ratio . The notes given to me are vague and before i start trundling through the internet i was wondering if anyone could explain it ?

Homework Statement Given a sequence of Heads and Tails, let’s say that the sequence has a switch each time one toss is different than the toss before it. For instance, the sequence HHTHTTTHTH has 6 switches. Suppose you toss a fair coin N times and record the resulting sequence of Heads and...

I really need help on how to solve this (Sweating): A dice game involves rolling 2 dice. If you roll a 2, 3 , 4, 10, 11 or a 12, you win \$5. If you roll a 5, 6, 7, 8, or 9, you lose \$5. Find the expected value you win (or lose) per game.

Hello all, I'm wondering if someone can offer some insight here: We have a random variable X, and it's expectation is called y. Can it be shown that 1/y = E[1/X] ?? Thanks

Homework Statement Does anyone know of a simple proof for this: https://s30.postimg.org/tw9cjym9t/expect.png E(X) = E(X|S)P(S) + E(X|S_c)P(S_c) X is a random variable, S is an a scenario that affects the likelihood of X. So P(S) is the probability of the scenario occurring and and P(S_c) is...

Homework Statement Let Y_1,Y_2 be independent random variable with uniform distribution on the interval [1,2]. Define X=max{Y_1,Y_2}. Find p.d.f., expected value and variance. Homework EquationsThe Attempt at a Solution Since $X=\max\{Y_1,Y_2\}$, this tells $Y_1$ and $Y_2$ must at most $x$...

Hello everyone! I'm confused because 90% and 35% obviously do not add up to 100% and as a result I'm really flustered! :C I appreciate the help and efforts of everyone on this website! :D

Homework Statement https://dl.dropboxusercontent.com/u/17974596/Sk%C3%A6rmbillede%202016-02-02%20kl.%2007.35.26.png I want to find variance matrix and expected variance vector of Y=(Y1,Y2). Y1 and Y2 are independant. Γ is the gamma function and ϒ is a known parameter. λ1>0 λ2>0 and ϒ>0...

Hello everyone, I'm stuck at a elementary stochastic problem. I have to calculate means, variance and co-variance for two random variables. Homework Statement Let r,g,b∈ℕ. r red, g green and b black balls are placed in an urn. The balls are then drawn one at a time with replacement, until a...

Consider a scenario where samples are randomly selected with replacement. Suppose that the population has a probability distribution with mean µ and variance σ 2 . Each sample Xi , i = 1, 2, . . . , n will then have the same probability distribution with mean µ and variance σ 2 . Now, let us...

"Let X be a Bernoulli random variable. That is, P(X = 1) = p and P(X = 0) = 1 − p. Then E(X) = 1 × p + 0 × (1 − p) = p. Why does this definition make sense? By the law of large numbers, in n independent Bernoulli trials where n is very large, the fraction of 1’s is very close to p, and the...

Hi, I need to minimize, with respect to \hat{y}(x), the following function: \tilde{J}_x = \mathbb{E}_{p(x,y)}[(\hat{y}(x)-y)^2] + \nu \mathbb{E}_{p(x,y)}[(\hat{y}(x)-y)tr(\nabla_x^2\hat{y}(x))] + \nu \mathbb{E}_{p(x,y)}[||\nabla_x\hat{y}(x)||^2], where x is a vector and y a scalar. I found this...

Homework Statement Consider a particle in an infinite square well potential that has the initial wave-function: Ψ(x,0) = (1/√2) [Ψ_1(x) + Ψ_2(x)] where Ψ_1(x) and Ψ_2(x) are the ground and first excited state wavefunctions. We notice that <x> oscillates in time. FIND the frequency of...

Problem Let X be a uniform(0,1) random variable, and let Y=e^−X. Find the CDF of Y. Find the PDF of Y. Find EY. Relevant Equations http://puu.sh/kAVJ8/0f2b1e7b22.png My attempt at a solution If I solve for the range of y I get (1, 1/e), but because Y is not an increasing function, my...

Homework Statement My teacher made up this question, but I think there's something wrong. Consider the wave packet in momentum representation defined by Φ(p)=N if -P/2<p<P/2 and Φ(p)=0 at any other point. Determine Ψ(x) and uncertainties Δp and Δx. Homework Equations Fourier trick and...

Homework Statement Markov process has probabilities p_{j,j+1} = 1-p_{j,0} = (\frac{j+1}{j+2})^k for j=0,1,2,... If T_j = min[n>1 : X_n=j] What is E[T(j)|X_0=j] for j=0,1,2,...? Homework EquationsThe Attempt at a Solution I figured that T(j)|X_0=j is j+1 but don't know how to work out the...

I have done a lot of counts but I'm sure that there will be a quicker way.. Can you suggest me? I have followed the way ##\bar{p}=-i \hbar\int \psi(x)* \cdot \frac{\partial}{\partial x} \psi(x) \ dx##... Can I follow a quicker way?

Homework Statement In my notes I keep stumbling upon this equation: Equation 1: E(X-bar^2) = (σ^2)/n + μ^2 I was wondering why the above equation is true and how it is derived.The Attempt at a Solution E(X-bar^2) ##Summations are from i/j=1 to n = E[(Σx_i/n)^2)] = E[(Σx_i/n)(Σx_j/n)]...

I know that the following is true and I've already proven it. Let $Y$ be a random variable and $\varphi$ a measurable function. Let $A$ be a $\Sigma_Y$ measurable set. If $ X (\omega) = \varphi(Y (\omega))$ for all $\omega\in A $ , then $\mathbb{E}(X|Y )(\omega) = \varphi(Y (\omega))$ for...

Given the PDF: f(x) = 1/12 , 0 < x <= 3 x/18, 3 < x <= 6 0, otherwise find the expected value, E(x). I know how to find the expected value if there was only one interval, but don't how to do it for two.

Hello all, I have this question, which I think I partially knows how to solve, but need some completion. "A man is playing versus a machine in the following way: The machine chooses 2 numbers randomly from the set of numbers 1,2,3,4,5, where a number can be chosen twice (with replacement). If...

Hi, I'm trying to show that Givien a probability triplet (\theta,F,P) with G\in F a sub sigma algebra E(E(X|G))=E(X) Now I want to use E(I_hE(X|G))=E(I_hX) for every h\in G since that's pretty much all I've for the definition of conditional expected value. I know this property should use the...

I’m working on a chemistry problem, which essentially translates to finding the answer to a related probability problem. However, my knowledge in probability is very limited and I'd be grateful if someone could help me out with it. The following is the problem:- Suppose I have a bag containing...

Consider N random variables X_{n} each following a Bernoulli distribution B(r_{n}) with 1 \geq r_{1} \geq r_{2} \geq ... \geq r_{N} \geq 0. If we make following assumptions of sets A and B: (1) A \subset I and B \subset I with I=\{1,2,3,...,N\} (2) |A \cap I_{1}| \geq |B \cap I_{1}| with...

Homework Statement If ##X\sim\mathcal{U}(-1,1)## and ##Y = X^2##, is it possible to determine to ##cov(X, Y)##? Homework Equations \begin{align} f_x &= \begin{cases} 1/2, & -1<x<1\\ 0, & \text{otherwise} \end{cases}\\ f_y &= \begin{cases} 1/\sqrt{y}, & 0<x<1\\ 0, & \text{otherwise} \end{cases}...

Hi guys, Suppose I have the function x = a + b -1 where a, b have expected values of 0.5 each. What is the expected value of x? is it 0.5 + 0.5 -1 = 0? or is it just 0.5 + 0.5? Secondly, suppose the same equation as above, x = a + b -1. If the variance of both a and b is 1/12, what is the...

Using a normal approximation method for the Wilcoxon Signed-Rank Test, I've seen that the expected value is \mu = \frac {n(n+1)}2 and the variance is \sigma^2 = \frac {n(n+1)(2n+1)}{24} . I'm wondering why these are the expected value and variance. I do recognize the formula for the sum of...

Definition/Summary A short introduction to expectation value is given, both for discrete and continuous cases. Equations For discrete probability distributions, <Q> \ = \ \sum _n Q_n p_n For continuous distributions specified by a normalized, real space wave-function \psi(x)...

We roll a pair of dice. If the sum of the dice is 7, you pay me $28. If the sum is not 7, I pay you the number of dollars indicated by the sum of the dice. What is the price that you should pay to play the game that would make the game fair?

Hey I am currently studying Quantum Mechanics and I have difficulty grasping a concept. I don't understand the following step in the derivation: \langle X_{A} \rangle=tr\left[\left(X_{A}\otimes I_{B}\right)\rho_{AB}\right] =tr_{A}\left[X_{A} tr_{B}\left[\rho_{AB}\right]\right] Thanks

Homework Statement two random variables have a join pdf f(x,y)= c , x^2+y^2<= 1, x >0, y>0 0, otherwise Find c. Find E{xy}. Homework Equations The Attempt at a Solution For the first part, since area= pi/4, c(pi/4) = 1 c=(4/pi) b) x=cos θ y= sin θ ∫∫-(sin...

Hello, i was wondering if the following is correct: The expected value of (a*x+b*x*y)/(c*y) given that a,b,c are positive constants and x,y are positive random variables is: ∫∫(a*x+b*x*y)/(c*y)*f_{x}(x)*f_{y}(y)dydx (where f_{z}(.) is the PDF of z). Thank you in advance.

Given $X$ as a negative binomial random variable with parameters $r$ and $p$. Find $E(\frac{r-1}{X-1})$. As $E(g(X))$ is defined as $\sum_{x\in X(\Omega)}g(x)p(x)$, this is my attempt in which I am stuck. What can I do next? In the case $y=r-1$, is the sum invalid? Thanks in advance!

Homework Statement Let x and y be discrete random variables with joint probability density function P(X,Y)= 2X-Y+1/9 for x=1,2 and y=1,2 0 Otherwise Calculate E[X/Y] Homework Equations E[XY]= ∫∫XYP(X,Y)dxdy The Attempt at a Solution I can't find a property...

Homework Statement Let x and y be independent random variables with E[x]=1, E[y]=-1, var[x]=1/2, var[y]=2 Calculate E[(x+1)2(y-1)2] Homework Equations E[x]=1=μ E[y]=-1=μ var[x]=1/2 =E[(x-μ)2] var[y]=2=E[(x-μ)2] The Attempt at a Solution Since x and y are independent...

I have an expected value problem where z is a desired expected value and I want to reach and x is an amount I can vary. There is a probabilty of success based on a logistic function ρ(x) with a reward of λx and failure with a probability of (1-ρ(x)) and loss of x. I am trying to solve for...

Homework Statement A machine consists of 2 components whose lifetimes are X and Y and have joint pdf, f(x,y)=1/50 w/ 0<x<10, 0<y<10,0<x+y<10 Calculate the expected value of X given Y=5. Homework Equations E[X|Y]= \int_{-inf}^{inf} x f(x,y)/f(y) dx The Attempt at a Solution...

Homework Statement Suppose that ∫X,Y(x,y) = λ2e-λ(x+y), 0 ≤ x, 0 ≤ y Find E(X + Y) Homework Equations E(X + Y) = E(X) + E(Y) The Attempt at a Solution Since the expected vale of a sum is the sum of the expected values, I attempted to find the marginal pdfs of the joint pdf...

Assume we have X\sim\exp(\mu,\sigma^2). How does one compute \mathbb{E}\left(Xe^X\right) and/or what is the outcome value?

Homework Statement I have that X is distributed with Gamma(a,b) and that Y = \frac{1}{X}. I found the pdf of Y to be \frac{1}{\Gamma(a)b^a} \left(\frac{1}{y}\right)^{a+1} e^{-1/yb} for y > 0. I need to use this to find the expected value. Homework Equations The gamma function is...

If a probability density function is fx(x) = 5x^4 for 0<x<1 and 0 elsewhere, then the expected value of E[x^0.5] is the integral of ∫x^0.5*fx(x) between 0 and 1 which is 10/11. However if I try to approach it as the expected value of Y=X^0.5 then I find fy(y) = 5*lny/y^4 and its expected...

Homework Statement We are given the following table and need to find the E(XY) X|Y y = 17 20 23 35 48 p(x) x = -20 0.02 0.03 0.07 0.02 0.06 0.2 0 0 0.05 0 0.05 0.1 0.2 1 0.05 0.03 0.02 0.07 0.03 0.2 3 0.01 0.02 0.03 0 0.04 0.1 17 0.18 0.04 0.06 0.01 0.01 0.3 p(y) 0.26 0.17 0.18 0.15...

Give me an example like: X: random variable representing the sum of 1 dice roll p: probability of getting a dice result E(X) = sum of X*p = 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) +6(1/6) BONUS POINT: what would be the E(X) for 3 dice rolls? Sorry, I am really dumb. I am...

Homework Statement What's the expected value of this problem (random variable)? X: represent the result of dice number 1 - result of dice number 2 example dice 1 first roll = 2; second roll = 3 dice 2 first roll = 1; second roll = 2 X = 2+3 -(1+2) = 2 what's the expected value...

Suppose I have the MGF moment generating function mx(t) = (e^t -1)/t How can I find EX?

Hi I know this may be a silly question but i am doubting myself on how i did this question: Suppose X and Y are independent, with E(X) = 5 and E(Y) = 6. For each of the following variables Z, either compute E(Z) or explain why we cannot determine E(Z) from the available information: Z =...

Homework Statement A man wants to travel to four cities (A,B,C,D) but he has such a bad memory that he can't remember the cities that visited, therefore, if he travel to city A he can choose between (B,C,D) and if he then travel to B he can choose between (A,C,D). Find v, If v it's the...

Homework Statement Hey! I got this problem about 3D harmonic oscillator, here it goes: A particle can move in three dimensions in a harmonic oscillator potential ##V(x,y,z)=\frac{1}{2}m\omega^2(x^2+y^2+z^2)##. Determine the ground state wave function. Check by explicitly counting that it is...