# expectation

1. ### Expectation with confidence

Hello, It has been a while since I used my probability and statistics. My question is: Say a group of 5 five people need to find the similarities between two foto's individually. After checking the result is that they found 3, 6, 2, 8, 1 correct similarities. How can you say with a certain...
2. ### Binomial expectation E(X|X>1)

General case: X~B(n,p) I could integrate the product of x and pmf from 1 to infinity and divide it by the integral of just pmf from 1 to infinity to find it, but I'm really stuck since I can't do it due to the sophisticated pmf function of binomial. How can we find this expectation and...
3. ### (URGENT!) Simulating expectations and a conditional expectation

I need to simulate a conditional expectation of the form: E (Xi^2 /(||X||^2 +h) | R^2 = ||X-T||^2 + ||U||^2 , Zi^2= (Xi - Ti)^2) Where X~N(T,I_p), U ~N(0,I_n) and ||.|| being the euclidean norm, i found this result using the nadaraya-watson approximation (https://arxiv.org/abs/1306.1182), but...
4. ### A statistic question.

Provider Charge(Total) Fraud %Fraud Fraud*%Fraud A §§§§§§§1000§§§§§§§600§§§§§0.6§§§§§§360 B §§§§§§§100§§§§§§§§70§§§§§§0.7§§§§§§49 C §§§§§§§10§§§§§§§§§8§§§§§§§0.8§§§§§§6.4 D §§§§§§§1§§§§§§§§§§1§§§§§§§1.0§§§§§§1 Please ignore "§" above. Which provider should be given alert? I am...
5. ### estimating expected value of a difficult cost function.

suppose i want to compute the following expectation: E = \int C(x)f(x)dx where x follows a known pdf f(x) from which we can easily draw samples, and C(x) is a function that is very difficult to compute for given x. As a result, i can not solve the integral analytically or numerically. Suppose...
6. ### Could someone verify my logic for managing probability distributions in an experiment

I'm not well versed in stats lingo, but am hoping my logic in the concepts here makes sense and is correct. Often in my work (measuring electrical responses of cells) I take of more than one independent measure per sample, such as the time to an event occurring, along with the size of that...
7. ### Randomized Block ANOVA

While reading through my lecture notes, I came across a randomized block ANOVA model and some assumptions. What intermediate steps did the authors use to obtain these assumptions (Expectation and Variance) from the given model?
8. ### Help with proof that expected value of x_i is the populaton mean X bar

I'm having a little trouble with the proof that the expected value of x_i is \bar{X} . What I have is E[x_i]=\sum_{j=1}^{N}X_j Pr(x_i=X_j) Then Pr(x_i=X_j) = 1/N This is the bit I can't understand, how does that probability evaluate to that value. I know the...
9. ### 4th-variance?

Hello any and all, I am no statistician so does the term "4th-variance" mean anything to someone? I am attempting to replicate the technique found in the publication below. The paper suggests that the 4th-variance is related to the expectation operator. The paper also discusses moment...
10. ### Understanding expectation operator notation

Hi, I am trying to understand how to interpret a problem that uses the expectation operator. Please see the attached pdf for more information. Could someone explain in words how to read the definition of Yk that uses the summation operator? Why would the mean of Y equal 0? I think I am...
11. ### unconditional expectation for GARCH model with normal inovations

Hi i have been asked to find unconditional expectations and then a recursive relation. I think I have started well but i am confused at how the recursive relation is made up. this is then to be used with a GARCH model i am working on. details of question: d(t) = mu + sigma(t)Z(t)...
12. ### Upper Bound Error for Expectation Approximation?

Dear all, I have a problem for the past few weeks and couldn't find the answer in the books or in the internet. I know that in general: E(g(X1, X2, ...)) is not equal to g(E(x1), E(X2) ,...) where E() is the expectation operator and g() is a function. For example E(XY) is not equal to...
13. ### cross term

The book says that the following cross term can be shown to be zero by iterating the expectation: E[(Y-E(Y|X))(E(Y|X)-g(X))]. What does it mean "to iterate the expectation"?
14. ### Online-estimate of squared correlation coefficient for linear optimization

Summary: Is there a way to directly estimate the squared correlation between two zero-mean Gaussian variables on-line and without storing more than two samples at any given time? Dear all, I am working on an optimization procedure to minimize the correlation between two zero-mean normally...
15. ### Expectation/probability question (sorta like Craps, maybe?)

I'll try to be as brief as possible: I have a number of events that can happen, say e1, e2...eN. N isn't particularly large. Each event has a probability of "failure", p1, p2...pN (Actually, there will likely be an overall failure rate, that will be converted to a weighted probability based on...
16. ### Properties of expectation

I am working on a pricing methodology under certain conditions. Suppose we have a population of size N and this population has a distribution of reservation prices f(p) . Now the problem of the firm becomes to maximize R = p N \int_p^{\infty} f(p) Or to maximize log(R) = log(p) +...
17. ### How to prove that the expectation and variance of a Poisson random variable = lambda?

This probably has an easy solution, but I was wondering if anybody could help me solve and explain these two questions: (a) Show that the expectation of the random variable is E(X) = lambda (b) Show that the variance of the random variable is Var(X) = lambda Any help would be very...
18. ### expectation problem

10 balls are inserted (uniformly) into five jars ..each insertion is independent from the others. compute E(X1*X2) where X1 and X2 describes the number of balls in each jar. so far: -P=Pr(Success from each jar poin of view=the ball was inserted into it)=1/5...
19. ### Basic Question

Hi all, I feel a little embarrassed about this, but: what is the rule linking the probability of an event A to the weighted sum of its sub-events? E.g. if A is a set of three events, {a1, a2, a3}, then P(A) = E(a*), right? Is it derivable from the axioms? Does this rule have a name? Thank...