Expected value Definition and 239 Threads

I'm bad at stochastics so really glad for any help Homework Statement I have two normally distributed NON INDEPENDENT stochastic variables X~N(muX,sigX^2) and Y~N(muY,sigY^2) A third variable D is defined as D = sqrt(X^2 + Y^2). Since Y and X are stochastic D will also be stochastic...

Homework Statement Hello, I was reading Feynman's lectures on physics, and I'm having trouble following some deductions in the part about Probability. The random walk is a problem in which someone starts at x = 0 ant then takes a step forward (x = 1) or backward (x = -1) and after N steps de...

Homework Statement 4: (T/F) The expected value of a distribution always occurs at the center of the tallest bar on the histogram. Homework Equations (no equation necessary for it is T/F) The Attempt at a Solution I believe this is false for the expected value can be definite or...

Homework Statement Find E[e^x] where x~N(\mu, sigma squared)Homework Equations The Attempt at a Solution It looks like a moment generating function. Here is what I did: Assume X= \mu + \sigma*Z E[etx]= E[et(\mu+\sigma*Z)] I simplified it and used the fact of moment generating functions...

Hello, I am having A LOT OF TROUBLE with this problem. Honestly, I did check my sources before coming here and I still cannot figure it out. =( Here it is: If each card has same points as their number (Ace is 1 point, 2 is 2 points, 3 is 3 points), then Jack, Queen, King each is 10...

Hi members, Hope someone can help with this assignment question? I need to proof: E(1/1+X) = [1-(1-p)^n+1]/p(n+1) where X ~ Bi(n,p) Below are my steps and I'm not sure where I went wrong: 1. sum(x=0 to n) (1/1+x)*(n choose x)*p^x*(1-p)^n-x 2. sum(x=0 to n)...

Homework Statement Consider a random variable X having cdf: 1, x ≥ 4, 3/4, 1 ≤ x < 4, FX(x) = 1/2, 0 ≤ x < 1, 1/4, −1 ≤ x < 0...

I have a 2x1 matrix A. I would like to find out E[A] which is the mean of the matrix. How do I do this? what is the dimension of the resultant matrix? using this E[A], I am going to find the covariance of matrix A by this formula cov(A) = E[(A - E[A])(A - E[A])^{T}) could someone please...

Homework Statement A sample of size n is drawn from a population having N units by simple random sampling without replacement. A sub-sample of size n_{1} units is drawn from the n units by simple random sampling without replacement. Let \bar{y_{1}} denote the mean based on n_{1} units and...

May I ask how come that E[\bar{X}^{2}] = \frac{\sigma^{2}}{n} + \mu^{2}?

So i a need to find E[XY], expected value of XY But the process of finding E[X] includes a long and tideous integral which i am trying to avoid. So computing E[XY] using its formula is also something i am trying to avoid. But could i use this identity? E[XY] = E[E(XY/Y)] = E[Y[E(X/Y)]]...

Hi guys, if X1,X2,...,Xn are independent and identically distributed random variables, how do you find E(max(X1,...,Xn))? Do you need to do order statistics or anything of that sort here? I got my answer by letting Y=max(X1,...Xn) and I got the CDF and then pdf of Y. For the CDF of Y, I just...

Homework Statement Whats a hint to solve E(min(X,100)), when X~Geometric(theta)? Homework Equations geometric distribution where p is theta The Attempt at a Solution I got here 99 summation x*theta*(1-theta)^x x=o + inf. summation 100*theta*(1-theta)^100 x=100 But I don't know what to...

Homework Statement The radial distribution factor for a 1s orbital given: R10 Calculate the expected value for potential energy of a He atom in the ground state. Homework Equations i understand the integral math where I solve down to <1/r> = z/a but now, how do i use the V(r) =...

Hello, I have a discrete random variable z whose expected value \mu is unknown. Its distribution is also unknown. We extract N samples z_1,\ldots,z_N, where each sample is an integer number: z_i\in \mathbb{Z}. Now, I introduce an estimator for the expected value defined as follows...

1. Suppose X is a random variable with probability function f(x) = 0.49x(0.3)^ (x-1). Find E(x). 2. E(X) = sum of all x of x*f(x) 3. so I know that E(X) = sum of all x of x*f(x) so E(x)= 0.49* sum of all x of x^2(0.3)^(x-1) But I'm not sure how do i evaluate the sum? Can...

Homework Statement If X~(-5,5) find E[||X|-2|] Homework Equations If a variable is distributed uniformly then f(x) = 1 / (b-a), with a mean of (a+b)/2. If x~u, then y~u. The Attempt at a Solution I think I should change the variable, so y = |X| - 2, and then find E[|y|]. So if I...

Homework Statement I'm trying to find the expected value of a probability distribution. Homework Equations \int_{-\infty}^\infty xP(x,t) = \int_{-\infty}^\infty x \frac{1}{\sqrt{4\pi Dt}}e^{-\frac{(x-dt)^2}{4Dt}}dx The Attempt at a Solution I expect the value to be something like...

An insurance company issues a one-year $1000 policy against an occurrence A that happens to 2 out of every 100 owners of the policy. Administrative fees are $15 per policy and not part of the companies profit. How much should the company charge per policy to make a profit of $50 per policy?

Homework Statement How to calculate the expected value of the log of a uniform distribution? Homework Equations E[X] where X=ln(U(0,1)) The Attempt at a Solution integral from 0 to 1 of a.ln(a) da where a = U(0,1) = -1/4 However I know the answer is -1

Homework Statement Let X be a continuous random variable with median m. Minimize E[|X - b|] as a function of b. Hint: Show that E[|X - b|] = E[|X - m|] + 2 \int (x - b) f(x) dx , where the integral is from b to m. Homework Equations The Attempt at a Solution I wanted to try a...

Thanks everyone!:) My Answer: If I understand it right, since there are 3 dice, the probability that any of the numbers 1 to 6 appears after the throwing the dice is 36/216 which gets simplified to 1/6. so the probability of winning back your dollar is 1/6 and losing it would be 5/6. so...

Hi all, I have a question of computing the expectation of random sums. E(sim_{k=1}^N X_k) = E(N)E(X) if N and X_1, X_2,...are independent and X_k's are iid. Here both N and X_k's are r.vs. But the condition of N and X_1, X_2,...being independent is not true in many cases. How will...

Hello friends, I am having some trouble with a particular statement an author made in a book. Despite being a statistics question, it is at its heart, a calculus question. Perhaps someone here with a better understanding of the subject can help, because I'm not convinced the matter has...

Hello forumers, I am studying some of the theory of Brownian motion and stochastic differential equations, and the author of the book I am using (https://www.amazon.com/dp/0521859719/?tag=pfamazon01-20) makes an argument which, despite a week's worth of attempts, I cannot seem to prove...

Homework Statement Suppose that a particle starts at the origin of the real line and moves along the line in jumps of one unit. For each jump, the probability is p that the particle will jump one unit to the left and the probability is (1-p) that the particle will jump one unit to the...

Homework Statement Suppose that a point is chosen at random on a stick that has length 15 inches, and that the stick is broken into two pieces at that point. Find the expected value of the lengths of the two pieces. Homework Equations E(x)=\sumf(x)xdx from -infinity to +infinity...

Hello, Just came across this that: E[cos(t)sin(t)] = 0 the expected value of the product of cos(t)sin(t) is 0. However, I am unable to convince myself that is the case. Can anyone help me understand why this is so? Many thanks, Luc

Homework Statement Suppose that passengers arrive at a train terminal according to a poisson process with rate "$". The train dispatches at a time t. Find the expected sum of the waiting times of all those that enter the train. Homework Equations F[X(t+s)-X(s)=n]=((($t)^n)/n!)e^(-$t))...

Hi All, i got a short question concerning the ev of a monotone decreasing function. when i got a nonnegative random variable t, then its ev (with a continuous density h(.)) is given by E(t)=[int](1-F(t))dt Then if v is a nonpositive random variable, is its ev given by...

suppose we have random variable defined a function of another random variable such that Y = \mathbb{E}(X) it seem then Y is a constant. then \mathbb{E}(Y) = \mathbb{E}(X) does this even make sense ?

Homework Statement Hi All, I have a homework question that I would like some hints on. I am given X and Y with uniform densities on [0,2], and Z := X+Y. The end goal is to find E[X|Z]. Now I know I can use symmetry to argue that E[X|Z] = E[Y|Z], and that E[X|Z] + E[Y|Z] = E[Z|Z] = Z, so...

Hello everyone, I'm evaluating the one-gluon-exchange tensor part of a phenomenological potential between two particles, and it involves a term like this: S_{ij}=3(\vec{\sigma_i}\hat{r_{ij}})(\vec{\sigma_j}\hat{r_{ij}})-\vec{\sigma_i}\vec{\sigma_j} With r_{ij} the unit vector in the...

EDIT: I found the solution, it can be done using the TwoVar() function on the TI-89 and it gives you a whole lot more than just the expected value. thanks anyways

Hello friends! Given an estimator of the population mean: \bar{Y}=\frac{\sum^{N}_{i=1}Y_{i}}{N} The expected value of \bar{Y} is : E(\bar{Y}) = \frac{1}{N}E(Y_{1})+\frac{1}{N}E(Y_{2})+\cdots+\frac{1}{N}E(Y_{N})=\mu where \mu is the population mean. Therefore: E(\bar{Y}) =...

Homework Statement Suppose that 15 observations are chosen at random for the pdf f(Y) = 3y^2 on the interval 0 to 1. Let X denote the number that lie in the interval (.5,1). Find E(X) Homework Equations The Attempt at a Solution Ok so to get the expected value u integrate the...

\langle p\rangle=-i\hbar\int \Psi^*\frac{\partial}{\partial x}\Psi dx Apparently, in general, we get a complex number for momentum. What does it mean, since p is an observable?

Find E(X) given the moment generating function M_X (t) = 1 / (1-t^2) for |t| < 1. (The pdf is f(x) = 0.5*exp(-|x|), for all x, so graphically you can see that E(X) should be 0.) ---- I know that E(X) = M ' _X (t) = 0 BUT M ' _X (t) = 2x / (1-x^2)^2 which is indeterminate at 0...

Homework Statement A catalog contains 10 itmes. Two people, A and B each select 3 items from the catalog independently. What is the expected value of the number of items A and B ordered. My attempt: Let A chose any 3 items. The probability that B Chose 1 similar item is 3/10 Chose 2 of...

Homework Statement If you throw exactly 1 head in three tosses of a coin you win $27. If not you pay $21. Homework Equations I know, E(X) = sum[x subscript i * P(X = x subscript i)] The Attempt at a Solution Sorry y'all I don't really know how to use all the fancy letters and...

Expected value: urgent help needed Homework Statement "Spin-and-Win" is under new management. The new management has created the spinner to the right and now charges $1 per spin. (The person spinning wins the amount pointed to by the spinner.) a) What is the expected value for this...

Hello there, yet another trivial problem: I've attended the 'stochastic process' course some time ago but the only thing I remember is that this kind of problem is really easy to compute, there is some simple pattern for this I presume. thanks for your help, rahl.

Hi, I want to derive an expression to compute the expected value for the product of three (potentially) dependent RV. In a separate thread, winterfors provided the manipulation at the bottom to arrive at such an expression for two RV. Does anybody have any guidance on how I can take this a...

Homework Statement A density function used is: f(y) = \frac{2y}{\theta}e^{\frac{-y^{2}}{\theta}} y > 0 using method of transformations find: (a) pdf of U = Y^2 (b) E(Y) and V(Y) Homework Equations f(u) = f(h^-1(u))*|dh^-1/du| h^-1(u) = sqrt(u) The Attempt at a Solution The...

If each card on a regular deck 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...what's the expected value of your opponent's hand if you deal them 3 cards? I know the empirical expected value...but...

here's a problem I'm a little confused by: a limo agency has limos with 4 seats but they book 6 for the same ride because they assume 20% are no-shows. what is the probability that someone will be denied a seat and what is the expected number of empty seats? i think for the second part the...

Prizes and the chances of winning in a sweepstakes are given in the table below. Prize: Chances $25,000,000: 1 chance in 400,000,000 $250,000: 1 chance in 150,000,000 $75,000: 1 chance in 50,000,000 $10,000: 1 chance in 4,000,000 $800,000: 1 chance in...

Hello, I have the following expression: G^2=\frac{\mathcal{E}_2}{\mathcal{E}_1\,\alpha+\mathcal{N}} where \alpha is an exponentially distributed random variable, and all other variables are constants. The authors said that, this expected value can be written as...

Hi, My question is related to this web page. http://en.wikipedia.org/wiki/Estimator_bias In the Examples section, note the equation for the expected value of sample variance. {E}(S^2)=\frac{n-1}{n} \sigma^2 Could anybody please show me the steps to go from the sample variance...

Homework Statement We have a linear combination of eigenstates of observable A \Phi_+ and \Phi_- with eigenstates a and -a. The expected value of the energy for both states is 0, while (\Phi_+,H\Phi_-)=E, with E real. Calculate the expected value of A for eigenstates \Phi_+ and \Phi_- over...