Questions tagged [expected-value]
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Questions about the expected value of a random variable.
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Expected number of ball tosses to have at least 5 balls in 4 out of 5 bins (Skyrim application)
I have a bit of an interesting probability question that has an application to Skyrim and the number of quests you need to complete to get an achievement for the Thieves Guild. I can generalize the ... probability expected-value- 41
What’s the expectation of one binomial random variable given the sum $n$ independent but non-identical random variables
Consider $n$ independent random variables $X_1, X_2, \cdots, X_n$ where $X_i \sim B(m_i, p_i)$ is a binomial random variable with probability $p_i$. Let $S = \sum_{i=1}^n X_i$ be the sum of these n ... probability random-variables expected-value conditional-expectation- 462
Expectation of a dt term
I am working with Hamilton-Jacobi-Bellman Equations and the following result appeared. Suppose $V_t= \frac{\partial V}{\partial t}$ and that $ E_{t}[Y]=E\left[Y \mid F_{t}\right] $ , where $F_t$ ... expected-value- 13
Number of expected heads in a row
As we know, the expected number of coin flips to get two heads in a row is 6, three heads in a row is 14. So my question is, is there any way to determine this? What are the expected number of heads ... probability expected-value- 1
Gradient of expectation under perturbation by uniform p-unit ball
Let $\mathcal{U}$ denote a uniform distribution. Let $\mathrm{B}_n^p$ and $\mathrm{S}_n^p$ be the $n$-dimensional $p$-unit ball and sphere, respectively. Then \begin{align} \nabla_\mathbf{x} \mathbb{E}... reference-request expected-value lp-spaces uniform-distribution- 5,100
Mistake in 'average size of smallest piece'
This is related to the question A bar is broken at random in two places. Find the average size of the smallest, of the middle-sized, and of the largest pieces. I have already seen related questions: ... probability expected-value- 21
How to Prove Removing a Below-Expectation Element Increases Expected Value
I am trying to prove that the expected value of Q will increase if I remove a below-expected-value element from the possibility space. While it seems intuitively obvious, I'm having trouble with the ... inequality solution-verification expected-value- 3
Find expected value for this problem!
Question: Two players are playing a game: there are $n$ pictures of famous celebrities in a box whose names are written behind it. Each time a picture will be taken out of the box and one of the ... probability probability-distributions random-variables expected-value- 157
What is the conditional probability $P(Y|X=x)$, where $Y$ is binomial with Poisson distributed $n=X$?
Question The number of patients visiting the dentist on a day follows a Poisson distribution with $\lambda= 20$. Patients can either have one or two issues, the probability of a patient having one ... expected-value conditional-probability conditional-expectation poisson-distribution binomial-distribution- 1
Union Bound of two events?
I am trying to understand the assumption proof of Theorem 2(Page -$7$) in the paper "A Universal Law of Robustness via isoperimetry" by Bubeck and Sellke. Inequality 1 \begin{align} \mathbb{... probability solution-verification expected-value upper-lower-bounds empirical-processes- 294
Prove equation $E(h(X)\,e^{-Y})=E(e^{-Y})\, E(h(X-\operatorname{Cov}(X,Y)))$
Prove: $$ E\bigl(h(X)\, e^{-Y}\bigr) = E\bigl(e^{-Y}\bigr) \, E\bigl(h(X-\operatorname{Cov}(X,Y))\bigr) $$ when $X$, $Y$ are both normally distributed, $h(X)$ is a function of $X$. I think it can be ... probability probability-distributions normal-distribution expected-value- 687
Does $E[X] = E[X|X < a]P\{X < a\} + E[X|X ≥ a]P\{X ≥ a\}$?
Question. Does $E[X] = E[X|X < a]P\{X < a\} + E[X|X ≥ a]P\{X ≥ a\}$? I would like some hint on how to start this, and mostly if this affirmation is true, whichever hint would help me a lot, I ... probability expected-value conditional-expectation- 91
Start with $1 and toss a coin. If it comes up heads your winnings double, if tails you lose all your winnings. What are the expected winnings?
You start with 1 dollar and toss a coin. If it comes up heads your winnings double, if it comes up tails you lose all your winnings. What are the expected winnings? This seems a variation of St. ... probability expected-value gambling- 121
How can I prove that $\Bbb{P}(X>0)\geq \frac{\Bbb{E}(X)^2}{\Bbb{E}(X^2)}$
I have the following problem: Let $X$ be a nonnegative random variable such that $\Bbb{E}(X^2)<\infty$ Then show that $$\Bbb{P}(X>0)\geq \frac{\Bbb{E}(X)^2}{\Bbb{E}(X^2)}$$ I would like to get ... probability probability-theory expected-value stochastic-calculus cauchy-schwarz-inequality- 1,509
Can I use the Chebychev inequality to prove this statement?
Let $X$ be a random variable with $\Bbb{E}(X^2)<\infty$ and $a>0$ I need to show that $$\Bbb{P}(X>a)\leq \frac{\Bbb{E}(X^2)}{a^2}$$ My idea was the following. Let me first remark that $$\{X&... probability probability-theory expected-value stochastic-calculus- 1,509
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