# expected-value's questions - English 1answer

1.127 expected-value questions.

### 2 Expectation of E(g(X + c))

1 answers, 46 views time-series expected-value
This is from Time Series Analysis from WS Wei If, where Approach - We have to find Var(Z) So, since and I have simulated this scenario on computer with and the answer seems to be ~ 0.5 ...

### 3 Expected Value: Decimal or Whole values?

Say you are given a sample size consisting of a number of whole objects, such as cats (n=20). You are asked what the expected value of some factor of these cats is (ex. how many are expected to be ...

### Lower bound on expectation of concave function

Let $X$ be a random variable, and let $f$ be a concave function. Are there any known lower bounds for (or methods of lower bounding) $\mathbb{E}[f(X)]$? Jensen's inequality only gives an upper ...

### 1 Explanation of proof for infinite variance in ordinary importance sampling for value function calculation

In the barto and sutton book, the authors have provided an Example on page 106, Ex 5.5 where they prove that the variance is infinite for an ordinary importance sampling method. In this derivation, ...

### 4 Expectation of the maximum of two correlated normal variables

I am curious what the derivation for the expectation of the maximum of two jointly normal random variables $X$ and $Y$ with correlation coefficient $\rho$. I could start with the following but the ...

### 19 Example of a non-negative discrete distribution where the mean (or another moment) does not exist?

4 answers, 1.513 views mathematical-statistics expected-value
I was doing some work in scipy and a conversation came up w/a member of the core scipy group whether a non-negative discrete random variable can have a undefined moment. I think he is correct but do ...

### Existence of random variables with certain properties

0 answers, 22 views random-variable expected-value moments
Can there exist two random variables such that - 1) Their means are not equal. 2) Their k-th order raw moments for all k>1 are equal.

### 2 Expected value of quotient of Poisson distributions

Let $X$ and $Y$ be independent random variables such that $X \sim \text{Poisson}(\lambda \cdot c)$ and $Y \sim \text{Poisson}(\lambda \cdot (1-c))$, where $c$ is a real number in $[0, 1]$. Is there ...

### 10 When do Taylor series approximations to expectations of (entire) functions converge?

1 answers, 2.649 views expected-value approximation
Take an expectation of the form $E(f(X))$ for some univariate random variable $X$ and an entire function $f(\cdot)$ (i.e., the interval of convergence is the whole real line) I have a moment ...

### 1 Find an unbiased estimator for theta

0 answers, 27 views expected-value unbiased-estimator
The random variable $X$ assumes values 1; 2; 3 with probabilities: $P(X = 1) = \theta^2$ $P(X = 2) = 2\theta (1-\theta ),\quad 0 < \theta < 1$ $P(X = 3) = (1 -\theta)^2$: If in a random sample ...

### Confused about finding expectation of vector multiplied by matrix

0 answers, 591 views expected-value linear-algebra
I am little confused regarding finding expectation of vector multiplied matrix. X is vector having mean $m_x \in \mathbb{R}^{N\times 1}$ and variance vector $s_x \in \mathbb{R}^{N\times N}$. $\phi$ is ...

### 3 Multiple interval ratio of E[X / (X + Y)]

0 answers, 59 views expected-value stochastic-processes
I have a sequence of interchanging on- and off-intervals, each pair identified by index $i$. The duration of the on-interval $i$ is represented by random variable $X_i$, and the duration of the off-...

### 1 Expectation with subscript [closed]

1 answers, 287 views expected-value notation
I have a question. A and B are normal distibutions. how to calculate $\operatorname{E}_{A,B}[A^2]$ does it scene that I drop the B in the statement or do I have to consider the B somehow ?

### 1 Mutually exclusive events reward [closed]

1 answers, 53 views probability expected-value
Say I have an unbiased coin and if I roll heads I get 40 pennies reward and If I roll tails I get 80 pennies. I believe the following is correct for the expected reward from one toss: ...

### Learning Expected value

0 answers, 43 views probability expected-value
We probably have played the game "Throwing Balls into the Basket". It is a simple game. We have to throw a ball into a basket from a certain distance. One day we were playing the game. But it was ...

### 4 Deeper proof of common expected value of random convex weights

0 answers, 74 views expected-value exchangeability
$\newcommand{\E}{\mathbb{E}}$Let a finite collection of exchangeable random variables $X_1,...X_n$ (some authors would call this collection "interchangeable" since it is finite, reserving "...

### Expectation of MSE multiplied by weight matrix equals the rank of the weight matrix

0 answers, 25 views expected-value matrix

### 1 Variance of continuous Random Variable negative?

2 answers, 59 views probability expected-value
I am having trouble finding the Variance for this question. The proportion of salt X left in the salt shakers at the end of the day at a crowded restaurant has a probability density function given ...

### 6 Simple question about notation

1 answers, 1.377 views expected-value likelihood notation

### 4 A list of tricks for calculating expectations?

2 answers, 1.358 views references expected-value mgf
Does anyone know of a good resource listing known tricks (with examples?) for calculating closed form expressions from messy expectations? (e.g., moment generating function, law of iterated ...

### 2 Expected Value of an AR(1) process

I saw the answer on this post and got confused about a couple things in its explanation. Mainly, I am unsure of How the poster immediately knows the process $X_t = c+\phi_1 Y_{t-1} + \epsilon_t$ is ...

### 2 Calculating inter-annotator agreement

Are there situations when it is allowed to omit calculating expected agreement but use only observed agreement as reliable measure? I have multi-label classification (in particular annotation of ...

### 2 Elo Ranking Expected Scores

1 answers, 77 views expected-value elo
I am implementing an Elo ranking system for fun and came across an example on Wikipedia that I can't follow: Suppose Player A has a rating of 1613, and plays in a five-round tournament. He or she ...

### 2 What does an expectation with respect to a policy mean in the reinforcement learning value function

I would like to know what the formal definition of the following expression is $$V_\pi(s) = \mathbb{E}_{\pi}(G_{t+1} | S_t =s)$$ What does it mean to have the policy in the subscript? How would I ...

### 1 Find an expectation of normal random variable

1 answers, 51 views probability expected-value
How can I find an expectation of random variable $\xi \sim \mathcal{N}(a,1)$, where $a$ is random variable: $a \sim \mathcal{N}(0,\sigma^2),\quad \sigma = \text{constant}$ ?

### 4 Show that if $E\psi(x-\theta)= 0$ then $P(X< \theta) \leq p \leq P(X \leq \theta)$

Define $$\psi(x)=\begin{cases} 1-p & x < 0 \\ 0 & x=0 \\ -p & x> 0 \end{cases}$$. I have to show that if $$E\psi(x-\theta)= 0$$ then $$P(X< \theta) \leq p \leq P(X \leq \theta)$$...

### Elements of Statistical Learning training set [closed]

I am trying to read the Elements of Statistical Learning Tibshirani, Hastie and Friedman, however I have a problem with understanding the expected (squared) prediction error ($EPE$) formula that they ...

### 1 How to calculate Expectation of Multivariate Gaussian with x drawn from another Gaussian distribution?

0 answers, 41 views normal-distribution expected-value
Say, there is a $n$-dimension multivariate Gaussian, $g(x) = N(x:\mu, \Sigma)$ where $\mu$ is $n$-dim mean vector, and $\Sigma$ is $n \times n$-dim covariance matrix. I would like to calculate "...