# Tag Info

### Why is average of a random subset the same of the initial set?

Here are two approaches. (1) Here is the calculation using just the definition of expectation. Let $X$ be $\{x_1,x_2,\dots,x_n\}$. Set $Y$ is a random subset of size $l$. We assume all subsets are ...
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### Player in casino

In the casino, the player is at the center of the action, navigating through a world of chance and excitement. With every spin of the wheel or flip of the card, anticipation fills the air as the ...

### Expected payout riddle: How to keep signature collectors from forging?

If I'm understanding this correctly, the agent gets back the $x$ they paid if they successfully complete a job, correct? If that is the case, here's my approach to the solution. If the agent forges 0 ...

### Probability that a specific card appears before turning up exactly two aces when turning cards from a random deck?

X is counting the number of cards being turned up, including the two aces in question. So the correct expression for $X$ should be: $$X = 2 + X_1 + X_2 +... X_{48}$$
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### Can Chernoff Bound Theorem be applied to functions of independent random variables

I think McDiarmid inequality is what you are looking for. https://en.wikipedia.org/wiki/McDiarmid%27s_inequality
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1 vote

If $X$ is discrete and $P(X>0)>0$ then there exists some $x_i>0$ such that $P(X=x_i)>0$. As $P(X\geq 0)=1$, $X$ cannot take on a negative value with a non-zero probability, because the sum ...
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### Expected payout riddle: How to keep signature collectors from forging?

If the agent doesn't forge any signatures, s/he makes $200$. We can compare that with forging one signature. In that case, if the checked signature is not forged the agent makes $202$ If the ...
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### Probability: Question about expected value with coins

None of the coins are more likely to be in any order than the other would you agree? So if we have 2 one dollar coins and 1 five dollar coin, we have FOO, OFO, OOF How many times does each coin show ...
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### Randomly choose $n$ numbers between $0$ and $1$. Add the smallest number from each repetition until the total is greater than 1. How many repetitions?

I don't think you can find a closed form solution for any $n$, but for small $n$ the closed form solution can be found: Like that answer you referenced, we first need the probability that the sum of ...
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### $T$ Pokemon trainers catch a Pokemon every day. How many days does it take until two trainers own Pokemons of the same species?

After $d$ days, there are $Td$ Pokemon caught, and $\binom T2d^2$ pairs of Pokemon owned by different trainers. Each pair has a $1/P$ chance of being the same kind of Pokemon. These collisions are ...
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### expected value of a two dice rolling game

Let $E$ denoted the expected payoff per roll. Considering only the rolls that either give us a dollar or we lose a dollar, there are $6+18=24$ possibilities. $\frac{6}{24}=\frac{1}{4}$ of those win us ...
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### The Facebook Birthday Problem（Birthday Problem Variation）

If you have $n$ friends, the probability that you have a friend with each birthday is $$\frac{{n\brace 365}\cdot 365!}{365^n}.$$ The notation ${n\brace k}$ refers to the Stirling numbers of second ...
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