Expected value Definition and 250 Threads

Here is the question: You are playing a gambling game (silly, yea I know). The first part of the game is to throw a die. If it comes up a 3, you move on. Otherwise, you lose. The second part of the game entails pulling a card out of a standard deck. If it is a heart, you win $100...

While reading the article:Law of the unconscious statistician, I came across a line and then a few lines after that, the expected value of a a function g(x) is said to be given by: ∫f(x)g(x)dx. However, if g(x) is not explicitly known, how does one calculate the integtral?

the random value X takes values 1,2,3... and has the X has geometric distribution with p=0.20 (This means that X can be interpreted as the time the first crown to repeated throws a coin coin lands heads with probability p.) what is the expected value E(X/X>=6)=? i use this type ...

we have a variable that takes values 1,...,6 with density: n 1 2 3 4 5 6 f(n) 0.1 0.2 0.1 0.3 0,176 0,124 What is the average price (expected value) of X under the condition that X is even? E(X/X=even)=k*P(X=k/X=even)=0.2*2+4*0.3+0.124*6 i am...

Homework Statement I have a wavefunction Cxe^{-ax^2} and I have to find the expected value of x. Homework Equations ∫_{-∞}^{∞} x^3 e^{-Ax^2} dx = 1/A^2 for A>0 The Attempt at a Solution I get an integral like this: <x>=|C|^2 ∫_{-∞}^{∞} x^3 e^{-Ax^2} dx After trying integration by parts...

I have to solve this exercise. Here are also my solutions but I don't know if they're correct. Let Ω ⊆ R ^ 2 a finite set of points in R ^ 2. Notation v_i = (x_i, y_i). Pr [] is a probability measure on either Ω. Random variables X, Y: Ω-> R project a point on the coordinate. For example Y(v_i)...

16 people Meet together at a party. Each pair of these individuals decide to chance whether you hailed by handshake or not (probability handshake = 0.40). On average, how many handshakes occur? X=handshakes if 1 and no handshakes if 0 X=X1+X2+X3+X4+X5+X6+X7+X8 and...

Homework Statement Consider first a free particle (Potential energy zero everywhere). When the particle at a given time is prepared in a state ψ (x) it has <x> = 0 and <p> = 0. The particle is now prepared in Ψ (x, t = 0) = ψ (x) exp (ikx) Give <p> at time t = 0. It can be shown that in...

A question on a multiple choice test has 6 answers which just one is right and the other wrong. If the amount of the correct answer is 10 points how many points should be substracted for a wrong answer so if nobody answers randomly choosing one of the 6 answers get, on average, 0 points...

A question on a multiple choice test has 6 answers which just one is right and the other wrong. If the amount of the correct answer is 10 points how many points should be substracted for a wrong answer so if nobody answers randomly choosing one of the 6 answers get, on average, 0 points...

What is the expected value of the following expression exp(|z+\mu|), where \mu is a real constant and z=x+jy such that x and y are independent Gaussian random variables each with zero mean and \sigma^2 variance. When I try to take the expectation, I couldn't obtain a gaussian integral, so I...

Homework Statement Suppose that if you are s minutes early for an appointment, then you incur cost s * $3, while if you are s minutes late, you incur cost s * $5. Suppose the travel time from your present location and the location of the appointment is a continuous random variable with...

Homework Statement Suppose X_1, ... , X_n are iid with pdf f(x,\theta)=2x/(\theta^2), 0<x\leq\theta, zero elsewhere. Note this is a nonregular case. Find: a)The mle \hat{\theta} for \theta. b)The constant c so that E(c\hat{\theta})=\theta. c) The mle for the median of the...

Dear All: Given two random variables X and Y, if I have established the relationship E[X]>=E[Y], does this necessarily imply that X must have a first-order-stochastic dominance over Y? I know that first order stochastic dominance implies that the mean value of the dominating random...

1. In scanning electron microscopy photography, a specimen is placed in a vacuum chamber and scanned by an electron beam. Secondary electrons emitted from the specimen are collected by a detector and an image is displayed on a cathode-ray tube. This image is photographed. In the past a 4- ...

Does μx mean the same thing as E[X]? Also, does σ2x mean the same thing as Var X?

Homework Statement Given: f(x) = 1/2 - 1/4 |d-x| where x is the deliver date If the actually delivery date from target date falls within the interval of 6 < x <8, an incentive award of C results. However if x < 6, a penalty of C1 is imposed, while if x > 8, the penalty is C2. Find the...

Homework Statement Let g(x) = \frac{1}{x+c}, where c is a positive constant, and x is a random variable distributed according to the Gamma distribution x\sim f(x)=\frac{1}{\Gamma(\alpha) \beta^\alpha} x^{\alpha \,-\, 1} e^{-\frac{x}{\beta}}. I wish to calculate the expected value of...

The Hamming distance(HD) between two strings of equal length is the number of characters that differ between the two strings at the same position, for example the HD between "gold" and "wolf" is 2; the MHD is between N strings and is equal to the minimum of HD's among all possible combinations...

Hi everyone. I am currently in a club that prepares students for technical interviews for jobs such as investment banking, private equity and hedge funds. One of our mentors assigned us this question and to be honest I really do not have an idea how to approach it. I'm not sure if I am...

Homework Statement Suppose the distribution of X2 conditional on X1=x1 is N(x1,x12), and that the marginal distribution of X1 is U(0,1). Find the mean and variance of X2. Homework Equations Theorem: E(X_{2})=E_{1}(E_{2|1}(X_{2}|X_{1}))...

Homework Statement (X,Y) has joint density f_X,Y ( (x,y) = (3/16)(x+2y) for 0<y<x , 0< x<2 Evaluate E(Z) where Z = (3X+4Y)/(X+2Y) Homework Equations The Attempt at a Solution Getting the marginal densities f_X (x) =(3/8)x^2 for 0<x<2 f_Y (y) = (3/2)+(3/4)y for 0<y<2 Would I find the...

1. A city has 74,806 registered automobiles. Each is required to display a bumper decal showing that the owner paid an annual wheel tax of $50. By law, new decals needed to be purchased during the month of the owner’s birthday. How much wheel tax revenue can the city expect to receive in...

Homework Statement I'm trying to solve the following question: You and n other people (so n+1 people) each toss a probability-p coin, with 0<= P \ <=1. Then each person who got a head will split some arbitrary amount of prize money, K, equally. If nobody gets a head, then nobody gets the prize...

Not long ago I was surprised to learn that when trying to maximize the expected long-term growth rate of your money, it is sometimes necessary to bet on an outcome that has negative expected value (in addition to outcomes that have positive expectation). See...

The formula for the expected value of a continuous random variable is E(x) = \int_{-\infty}^{\infty} x\cdot f(x). This leads me to believe that the expected value of a function g(x) is E(x) = \int_{-\infty}^{\infty} g(x)\cdot f(g(x)). However, the correct formula is E(x) =...

Homework Statement Suppose that f_{X,Y}(x,y)=\lambda^2e^{-\lambda(x+y)},0\le x,0\le y find E[X+Y]Homework Equations The Attempt at a Solution I just want to double check I didn't make a mistake: E[X+Y]=E[X]+E[Y]=\int_0^{\infty} x{\lambda} e^{-\lambda x} dx + \int_0^{\infty} y{\lambda}...

Homework Statement Find the expected value of a continuous variable y with pdf fy= alpha*y^-2, 0<y<infinity. I know it is the integral from zero to infinity of y*fy, but I don't know where to go from there. I'm then supposed to use the expected value to find the method of moments...

Suppose that nx is binomially distributed: B((n-1)p, (n-1)p(1-p)) I wish to find the expected value of a function f(x), thus \sum_{nx=0}^{n-1} B() f(x) Assume that f() is non-linear, decreasing and continuous, f(x) = c is [0,1] to [0, ∞) I want to show that the above sum converges to f(p)...

The expected value of a random variable is not necessarily the outcome you should expect. For discrete probability it might not even be a possible outcome for the experiment. So what does the expected value mean intuitively? I will use and example because it helps me formulate my question...

Homework Statement A miner is trapped in a mine containing three doors. Door 1 leads to safety after 3 hours. Door 2 leads back to the mine in 5 hours. Door 3 leads back to the mine after 7 hours. What's the expected length of time until he reaches safety? Homework Equations X = amt of...

Homework Statement Prove that if X is a positive-valued RV, then E(X^k) ≥ E(X)^k for all k≥1 The Attempt at a Solution Why do I feel like this is a counter-example: X = {1,2,4,8,16,...} (A positive-valued RV) m(X) = {1/2,1/4,1/16,1/32,...} (A distribution function that sums to one) Yet...

I want to calculate \int_a^b \frac{1}{\sqrt{2 \pi \sigma^2}} e^{(-(x-\mu)/\sigma^2)} log_2 (1 + e^{-x}) dx

Hi, I have been learning/experimenting with the Martingale betting system recently. I have read a lot about how no "system" works for betting in casinos. However, I want to either prove or disprove the validity of the system by looking at its expected value/payout. I will be using the game of...

Homework Statement Given an initial (t=-∞) Fock state , \left|n\right\rangle, and a function f(t), where f(±∞)=0, show that for a Harmonic Oscillator perturbed by f(t)\hat{x} the difference \left\langle H(+∞) \right\rangle - \left\langle H(-∞) \right\rangle is always positive.Homework Equations...

Often in quantum mechanics, there appears statements of the type : Expected value of operator = a value I am told that operators are instructions and I do not understand how an instruction can have a value, expected or otherwise. Even in the case where the operator is of the form "muliply...

Homework Statement z = 2, P(Z=z)=1/6 z = 3, P(Z=z)=1/6 z = 5, P(Z=z)=1/6 z = 7, P(Z=z)= x z = 11, P(Z=z)= y I'm supposed to find x and y given that E(Z)= 5+2/3 I have no idea how to do this. All I got is 7x+11x=4 but I can't solve this

Homework Statement Suppose that X takes on one of the values 0, 1, and 2. If for some constant c, P{X = i} = cP{X = i - 1}, i = 1, 2. Find E [X] Homework Equations The Attempt at a Solution I'm not sure how to start this. A push in the right direction would be awesome. Thanks!

A has two bets(red or black) in a game of roulette. She bets half of what she has in the first round and then half of what she is left with after the first bet in the second bet. What is the expected value if she wins both bets? Is this correct? (n is what the player has originally)...

Homework Statement A computer code consists of two blocks written independently by two programmers. Each block contains no errors with probability 0.6, one error with probability 0.3, and two errors with probability 0.1. a. What is the probability that there are more errors in the first...

Let W_1 and W_2 be independent Chi-Squared distributed random variables with v_1 and v_2 degrees of freedom, respectively. Then F = (W_1/v_1)/(W_2/v_2) = (v_2/v_1)(W_1/W_2) is said to have an F-distribution with v_1 numerator degrees of freedom and v_2 denominator degrees of freedom. I want...

I am going to try to keep this short, so please advise whether I need to provide more detail for my question to make sense. In calculating the expected value of a lottery ticket, one must consider the possibility that more than one ticket is sold bearing the winning combination. One way to...

Hello everyone, I have the following question. Suppose that X and Y are independent and f(x,y) is nonnegative. Put g(x)=E[f(x,Y)] and show E[g(X)]=E[f(X,Y)]. Show more generally that Integral over X in A of g(X) dP = Integral over X in A of f(X,Y) dP. Extend to f that may be negative. I've...

Homework Statement I need to know these formulas to answer the homework problems, but I can't squeeze the forumlas out of the gibberish in the book, so I'm asking for varification of the formulas. For a bivariate probablity density function, for example f(x,y)= 2xy when x and y are...

Hi, I have to work with Expected Values and I am extremely confused over the following: In the part of my book that teaches me about Probability Distribution, in order to calculate the Expected Value I have to: Lets say we toss a coin twice. We can get 0 Heads, 1 Heads or 2 Heads I then draw...

Hi all Sorry for reposting, the previous post wasn't clear enough, it's my mistake, I'll make the question more clear, I found lot of people asking the same question on the Internet. Given that X is random variable that takes values: 0.....H-1 The PMF of X is unknown, but I can tell...

Homework Statement Show that E[Y^4] = 3, where Y~N(0,1) Homework Equations E[(Y-mu)^4]/[E(Y-mu)^2]^2 = 3 E(Y^4) = 1/sprt(2pi)*intregral (y^4)*e^(-y^2/2) The Attempt at a Solution I have expanded and simplified the first equation above and cannot get it to equal 3. I think it's...

Homework Statement Point is chosen at random (uniform PDF) within semi-circle: {(x,y)|x2+y2≤r2, y≥0} Basically, I'm supposed to find E[X] for this problem 2. The attempt at a solution I know how to do it, in a very long-winded fashion (find fY(y), and E[X|Y=y] etc). But my teacher says that...

Homework Statement Why is \langle p^2\rangle >0 where p=-i\hbar{d\over dx}, (noting the ***strict*** inequality) for all normalized wavefunctions? I would have argued that because we can't have \psi=constant, but then I thought that we can normalize such a wavefunction by using periodic...

In the notes we had the following example of a problem, with solution: Example. Shooting stars. If you watch the sky form a peak of "Kékes-tet˝o" (highest peak in Hungary) around midnight in August, you will see shooting-stars. Assume that the amount of time between two shooting-stars...