# expected-value's questions - English 1answer

1.075 expected-value questions.

### How can I find the expected value of these dependent values?

1 answers, 48 views expected-value markov-process
Okay so there's a game, where you have 1 percent chance of winning an alpha pack and if you fail you your chance goes up by 3 percent. How would you calculate the expected value? I've only taken an AP ...

### 1 Expectation Help

1 answers, 20 views self-study expected-value
I am having trouble a question in my probability course and was looking for some insight into it. A digital clock sits next to your bed and in the mornings when you don't use an alarm you notice Y =...

### Expectation of random sum of dependant variables

The expectation of random sum of independent identically distributed variables is given either by the law of total expectation or by Wald's identity. Are these generalised to tackle the random sum of ...

### 3 Expected value of a conditional probability

I am reading this article: https://www.sciencedirect.com/science/article/pii/S0040580901915424?via%3Dihub Where as far as I can make out they are taking the expected value of the difference of 2 ...

### 8 Expected value of ratio of correlated random variables?

For independent random variables $\alpha$ and $\beta$, is there a closed form expression for $\mathbb E \left[ \frac{\alpha}{\sqrt{\alpha^2 + \beta^2}} \right]$ in terms of the expected values and ...

### Unit Step Functions

0 answers, 9 views random-variable expected-value
The image below shows the process for calculating the Expected value of a squared random variable X. From line 3 to 4 the unit step function [u(x) - u(x-1)] is removed and a 3 is placed before (1-x^2)....

### 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 ...

### What's the best estimator for expectation if we can draw samples iid *and* we know the likelihood of each sample we receive

Suppose that $X_1, X_2, \ldots X_n$ is a sequence of random variables on a set $S$, drawn independently according to the pdf $p : S \to [0,1]$. Part I: Given some $f : S \to \mathbb{R}$, I want to ...

### 1 Is there any simple way for the expectation of squared of ratio of random variables?

0 answers, 23 views random-variable expected-value
So, for two random variables $A$ and $B$, I know that $\mathbf{E}[A]$, $\mathbf{E}(B)$, $Var(A)$ and $Var(B)$, I also know that $\mathbf{E}[A] = \mathbf{E}(B) + C$, I wonder if I can find a simple way ...

### 1 I still don't agree that E(X+Y)=E(X)+E(Y)

If the two random variable functions are non-independent, then it doesn't make sense why the equation holds true. For example, let's create a table: \begin{align} f(x,y) & \\[5pt] f(0,0) &= 0....

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

4 answers, 1.245 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 ...

### 35 Why is expectation the same as the arithmetic mean?

I am a beginner in statistics and probability study. Today I came across a new topic called the Mathematical Expectation. The book I am following says, expectation is the arithmetic mean of random ...

### 3 Mean of a Pearson Type VI distribution

I have a question that gives me the density of a Pearson type VI distribution and then says to state the range of parameter(s) for which the expression for the mean is valid. In your calculations, ...

### 2 Expected value of Log Gamma function transformed Poisson random variable

0 answers, 41 views poisson-distribution expected-value

### 4 Fourth order moments of the sum of multivariate normal distribution

Suppose $X\sim \mathcal{N}_d(\boldsymbol{0},\boldsymbol{\Sigma})$ follows a $d$-dimensional multivariate normal distribution. Let $\text{A}_i$ and $\text{A}_j$ be two arbitrary symmetric $d\times d$ ...

### 10 Are there any distributions other than Cauchy for which the arithmetic mean of a sample follows the same distribution?

If $X$ follows a Cauchy distribution then $Y = \bar{X} = \frac{1}{n} \sum_{i=1}^n X_i$ also follows exactly the same distribution as $X$; see this thread. Does this property have a name? Are there ...

### 1 Geometric interpretation of mathematical expectation of a random variable

Is there any nice geometric interpretation of the mathematical expectation of a random variable (preferably based on density or cumulative density plot)? (For example, median has a nice geometric ...

### Fundamentals of applied statistics [duplicate]

I'm a begginer in statistics. I came across a problem, please help me out. Is expectation always mean arithmetic mean of a variable?

### Need help with expected value calculation in coupon collectors in coupon collectors variant

I am revisiting a question I asked previously with a slight caveat. In my new situation, I am considering the marbles to always be attached to the same neighbors. Hopefully this will be clearer with a ...

### 4 Why do we use conditional expectation vs regular expectation in regression?

What is the significance of using conditional expectation E(Y|X=x) in regression and not just use the regular expectation E(y). What will be the consequence if we use E(Y) instead? ( can we do this ...

### 4 One-sided measurement error: $\widetilde{X} = X - \eta$, $\eta\geq0$. Is $E[X|\widetilde{X}=\widetilde{x}]$ increasing in $\widetilde{x}$?

Let $X\geq0$, $\eta\geq0$ and $X,\eta$ independent. We measure $X$ with a one-sided error: $\widetilde{X} = X - \eta$. Is $E[X|\widetilde{X}=\widetilde{x}]$ increasing in $\widetilde{x}$?

### 10 Expected value as a function of quantiles?

I was wondering where there is a general formula to relate the expected value of a continuous random variable as a function of the quantiles of the same r.v. The expected value of r.v. $X$ is defined ...

### 3 Expected value of a marginal distribution when the joint distribution is given

I am asked to find the expected value of a vector of two random variables when the joint density is given. Is the recipe for solving this problem: Find the marginal distributions Find the expected ...

### Expectation of Maximum Value

I'm trying to understand the basic statistics involved in trading. Suppose I'm trying to decide whether to buy a stock whose current price is $V_0$. Suppose I have some fancy statistical model from ...

### Expected value of counting function over infinite set

You have a random variable $X$, which can take a value from $i = \{1,2,3,...\}$, where the probabilities are $p_i = 0.5^i$. Now you if we have a list $(x_1, ..., x_n)$ of independent observations of ...

### 2 Why is Expected value of a random variable equal to the mean

This is a derivation I found online for the mean of a random variable: Let $X_1, X_2, \dots, X_n$ be $n$ independently drawn observations from a distribution with mean $\mu.$ Let $\bar X$ be the ...

### Determining average life expectancy from a simple model

0 answers, 13 views expected-value median life-expectancy
I'm trying to determine the average life expectancy from the following model. I feel I'm close, but I can't quite get the right answer. The daily death chance for any given individual is modeled as: ...

### Do discriminative models model conditional expectation?

In Machine Learning classic models like MLP, Logistic Regression or Linear Regression are called discriminative models. I frequently read that those models estimate the conditional probability ...

### Difference between predicted value and expected value for binary model

For a binary model with Y as the dependent variable and X1, X2, and X3 as independent variable, my understanding is that the predicted value is the value of Y at specified values of of X1,X2,X3. Ex. ...

### 5 $\mathbb{E}(\log(X_{max}/X_{min}) )$ of Weibull(alpha, 1)

1 answers, 88 views expected-value weibull
I'm trying to find the expectation of log(max/min) from n samples of Weibull(alpha, 1). But I keep failing. Can anybody give some hints? I tried: \$\mathbb{E}(\log(X_{max}/X_{min}) ) = \int_0^{\...

### 1 Find the expected frequency of some state in a state sequence of length N given a transition matrix M

I can represent stochastically-articulated sequences of states using a transition matrix M where a given entry in cell (i,j) corresponds to the probability of state j given that the current (or, most ...