Expected value Definition and 250 Threads

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...

Is the expected value E[x]or E[y] of a bivariate pdf fXY(xy) \int x f(x,y)dx or E[y] \int y f(x,y)dy ? example if f(x,y) = x+y E[X] = \int x *(x+y)dx regards Brendan

Homework Statement Let the join probability density function of ZX and Y be given by f(x,y)=\left\{\stackrel{2e^{-(x+2y)}\ \ \ \ \ if\ x\ \geq,\ \ \ y\ \geq\ 0}{0\ \ \ \ \ \ \ otherwise} Find E(X^{2}Y) Homework Equations I approached this problem using a theorem from the book that states...

Homework Statement Given Y1 and Y2 are integer values, where 0\leqY1\leq3, 0\leqY2\leq3, 1\leqY1+Y2\leq3 p(Y1, Y2) = \frac{{4 \choose y_1}{3 \choose y_2}{2 \choose {3-y_1-y_2}}}{{9 \choose 3}} Find E(Y1+Y2) and V(Y1+Y2) Homework Equations E(Y1+Y2) = E1(Y1)+E2(Y2) E1(Y1) =...

Homework Statement Let Z be a standard normal random variable, f is a measurable function and a is a constant. Show E[Zf(e^aZ)] = aE[e^aZ]E[f'(e^(a(Z+a))] Homework Equations The Attempt at a Solution I set up an integral from negative to positive infinity of...

Hi all. I'm struggling with this HW question. I've searched through the textbook and on the web and have been unable to find a solution Homework Statement I've got 4 i.i.d. random variables, X1, X2, X3, X4. Uniformly distributed on [0,1] so the pdf = 1 and cdf F(x_i) = x_i Let Y3 = the third...

Hello, Can someone please tell me whether I can use negative binomial distribution for this question. "If there are 3 types of books in a bookstore and each book has an equal probability of being bought. What is the expected number of purchases to get all 3 books?" Using negative...

Assume that two random variables (X,Y) are uniformly distributed on a circle with radius a. Then the joint probability density function is f(x,y) = \frac{1}{\pi a^2}, x^2 + y^2 <= a^2 f(x,y) = 0, otherwise Find the expected value of X. E(X) = \int^{\infty}_{- \infty}\int^{\infty}_{-...

Homework Statement Let X be the number of different birthdays among four persons selected randomly. Find E(X). Homework Equations The Attempt at a Solution I am not completely sure how to start this problem. I was thinking of trying to figure out the total number of combinations...

Homework Statement The distribution function of a random variable X is given by F(x) = { 0 if x < -3 3/8 if -3 \leq x < 0 1/2 if 0 \leq x < 3 3/4 if 3 \leq x < 4 1 if x \geq 4 Calculate E(X), E(X^{2} - 2|X|), E(X|X|). Homework Equations The Attempt at a...

1. Homework Statement [/b] A charitable organization is raffling a trip worth $500 to raise money and needs to decide which of the following scenarios would be the most profitable based on expected value of the proposed game. Case A: 3,000 tickets are sold at $1.00 each. Case B...

Homework Statement X and Y are joointly distributed discrete random variables with probability mass function pX,Y(x,y)=(c/ec)(1-c)xcy/y!, x,y=0,1,2,..., 0<c<1 Find E(XY) Homework Equations The Attempt at a Solution By definition, E(XY) ∞ ∞ = ∑ ∑ xy (c/ec)(1-c)xcy/y! x=0...

To find the expected value of Q(x,p) we evaluate <\psi|Q(x,-i\hbar \frac{\partial }{\partial x})|\psi>. But what do you do if you want to find, say, <p^(3/2)>. How do you raise the derivative operator to the three-halves?

This is more of a general question... let's say we have a wavefunction \psi, and we want to find the expected momentum, \langle p \rangle , of the state. Isn't this just \langle p \rangle = \int_{-\infty}^{\infty} \psi^* i\hbar \frac{\partial \psi}{\partial x} Now, if the wavefunction happened...

I have the following question: 2 persons shoot it each other. Person A shoots at Person B, if A misses, B shoots at A and so on. The Game continues until one of them hits the other one. Probability that A hits B is P1 ,and probability that B hits A is P2. I need to find the E[X]. They give...

This is for a discrete math homework set. 1. Suppose the cards in a deck are given the following values: Ace has value 1, two has value 2,..., ten has value 10, Jack has value 11, Queen has value 12, and King has value 13. A player selects a card. If it is a heart, the player receives half...

Homework Statement I have to calculate the expected value of the Hamilton operator (average energy) of a two, non interacting, identical particle system. Thus these particles can be bosons or fermions, but at the moment I just want to look at fermions. Homework Equations...

Homework Statement Given a unit square and a 'target' square of size LXL = p^2 < 1 in the unit square. The center of target square in equally likely to be anywhere in the unit square. What is the average size of the target square as a function of p^2. This is the problem and I have included a...

Given a unit square and a 'target' square of size LXL = p^2 < 1 in the unit square. The center of target square in equally likely to be anywhere in the unit square. What is the average size of the target square as a function of p^2. This is the problem and I have included a jpeg illustration...

Hey, I know how to find the expected value from the density function when it is in the form: (example) | y^2 -1<y<1 | fy =| | 0 elsewhere Ey = integral(upper limit 1, lower limit -1)[y*y^2 dy) but, what if the density function looks like this...

Hey, I know how to find the expected value from the density function when it is in the form: | fy =

Hi - I have a Pareto distribution X (xm=1, k known)*. High-value samples are filtered out and I want the expected value of the remaining. Namely: E[X|X<a]. *Wikipedia notations Many thanks in advance. Xavier

Let X be a set with n elements, and let A,B be subsets of X. What is the general expected value for the intersection of these two sets? Here for each n, we must find the possibility of having an intersection set of elements, multiply this probability by n, and then sum up the products we...

E[X]=2 Var(X)=3 Find E[4+4x+x^2] I'm just confused what its asking. The expected value of this function is 2 so the average of it is 2 and the variance is how much it varies which is 3? Every example I have for expected values is related to an example such as cards, not just a polynomial

E[X]=2 Var(X)=3 Find E[4+4x+x^2] I'm just confused what its asking. The expected value of this function is 2 so the average of it is 2 and the variance is how much it varies which is 3? Every example I have for expected values is related to an example such as cards, not just a polynomial

[problem] Consider n independent flips of a coin having prob p of landing heads. Say a changeover occurs whenever an outcome differs from the one preceding it. E.g., H H T H T H H T means 5 changeovers. What is the expected number of changeovers for an arbitrary p? [s0lution] see...

Around 3 years back, I had a stall setup at my school's fun fair. It was a simple gambling setup. You put your money on either of 3 things: i] Above 7, ii] Lucky 7 or iii] Below 7. And then, you roll the dice [2 of 'em]. If you put on either below 7 or above 7 and the dice sums up to below 7...

Can someone help me with this problem? The joint probability mass function of X and Y, p(i,j)=P{X=i,Y=j}, is given as follows p(-1,-2)=1/9, p(-1,-1)=1/18, p(-1,0)=1/12, p(-1,1)=0, p(0,-2)=1/12, p(0,-1)=1/9, p(0,0)=0, p(0,1)=1/8, p(1,-2)=0...

Homework Statement Given a square with side lengths X, where X is a random variable with some probability density function (the actual pdf is not important for my question). Why isn't the expected value of the area = E[X]^2 = E[X^2]? Homework Equations The Attempt at a Solution...

Hello, just a bit insecure about my answer. Problem:------- Suppose n people have throat cultures, and the cultures are then completely mixed up. If we randomly pair off the n peoples’ names with the n cultures, what is the expected number of correct labels? --------------- So, here's my...

Homework Statement A client is trying to connect to a web server on an overloaded machine that only accepts an average of one in 20 connections. How many times would the client expect to try before getting a connection? Explain your answer. The Attempt at a Solution This is part 5 of...

Homework Statement There is k carps in the pool, m of them are marked. I randomly fish out n carps and see that x of them are marked. What is the expected value of number of carps in the pool? (ie. expected value of number of the carps in the pool in the beginning) How will the...

I know that with an Hermitian operator the expectation value can be found by calculating the (relative) probabilities of each eigenvalue: square modulus of the projection of the state-vector along the corresponding eigenvector. The normalization of these values give the absolute probabilities...

Expected Value -- Please Help Hello, I have this question that is bugging me to death. Ok here it is: If a coin was flipped a maxium number times of five. What is the expected value for the number of flips required to get either 3 heads or 3 tails. I know the probability of head or...

Hey.. I am having some problems with this homework question, i thought perphaps somebody can help me on it. -- Let X be a random variable with probability mass function x P(x) -1 p 1 1 - p Find the value of the constant C not equal to 1 such that...

The usual expression of the expected value of X is: E[X] = (sum) x*p(x) i'm supposed to show that, for X a random non-negative discrete random(stochastic) variable, we have that: E[X]=(sum: i from 1 to infinity) P(X>=i) i have absolutely no idea how to do this. does anyone want to push...

Here goes: A potential customer for an 85000 dollar fire insurance policy possesses a home in an area that according to experience, may sustain a total loss in a given year with probability of .001 and a 50% loss with probability .01. Ignoring all other partial losses, what premium shoud the...

Let X be a random variable with Uniform(0,1) distribution. Let Y = X^2 + 1. Compute E[Y]. The question here is if I should compute the expected value of Y integrating from 0 to 1 for x(x^2 + 1)dx?

The prizes that can be won in a sweepstakes are listed below together with the chances of winning each one. $5900(1 chance in 8100); $2500( 1 chance in 6200); $600 (1 chance in 4700); $300(1 chance in 2600) Find the expected value of the amount won for one entry if the cost to enter is 75...

ok, so to find the expected value of fy(Y) = 3(1-y)^2 for 0 <= 1 <= 1 I thought the formula is y * fy(Y) which is the intgeral from 0 to 1 of y* 3(1-y)^2. right? the book says the answer is 1/4...but I get a whole number answer...

In a series of three binomial trials with p=.4, a random variable, X, is assigned to the outcomes to form a base 2 number, with 1 associated with success(S), and 0 associated with failure(F). For example, SFS->101=5. A) Find the expected value of X, E[X]. (Answer 2.80) B) Find the...

I'm supposed to prove that in a geometric distribution, the expected value, \mu = \frac{1}{p} without the use of moment generating functions (whatever that is) I start off with the very definition of the expected value. \mu_x = E(x) = \sum x \cdot p \cdot (1-p)^{x-1}...