3 votes
Accepted

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 ...
Aig's user avatar
  • 4,541
2 votes
Accepted

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 ...
Otis's user avatar
  • 94
2 votes

Expected value of number of specific cards in starting hands in a card game

Using the basic identity $$ n× C_n^r=r C_{n-1}^{r-1}, \tag{1}$$ we have $$\sum_{n=0}^s n × C_n^r×C_{s-n}^{b}=\sum_{n=1}^s r C_{n-1}^{r-1}×C_{s-n}^{b}=\\r\sum_{i=0}^{s-1} C_{i}^{r-1}×C_{s-1-i}^{b}=r C_{...
Amir's user avatar
  • 5,134
1 vote

Expected value of number of specific cards in starting hands in a card game

An easier way to solve questions like these is with an Indicator Random Variable $ X_i = \begin{cases} 1 & \text{if event } A \text{ occurs}, \\ 0 & \text{otherwise}. \end{cases} $ In this ...
Otis's user avatar
  • 94
1 vote

Expected value of number of specific cards in starting hands in a card game

If you have 40 players with one card each, then all cards are dealt. The expected value of red cards handed to all players is r. Since each player is in an identical position, each has the same ...
gnasher729's user avatar
  • 10.1k
1 vote

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
Ibra's user avatar
  • 140
1 vote

Simple question about expectation

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 ...
Julio Puerta's user avatar
  • 4,801
1 vote
Accepted

Expected value and average value problem

If $$1-\Pr\left\{ 0.64\leq X\leq0.66\right\}$$ $$=1-\Pr\left\{ \dfrac{0.64-\mu}{\sigma/\sqrt{n}}\leq\dfrac{X-\mu}{\sigma/\sqrt{n}}\leq\dfrac{0.70-\mu}{\sigma/\sqrt{n}}\right\},$$ then $$\Pr\left\{ 0....
AOS's user avatar
  • 181

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