All Questions
Tagged with expected-value binomial-distribution
42
questions
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Expectation of binomial random variable
Having trouble understanding something I read in a paper recently.
Say we have $X \sim \operatorname{Binomial}(N,p).$ The paper states:
$$E[X \mid N,p] = Np$$ (so far so good)
and
$$E[X] = \mu p$$
...
- 23
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46
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I would like some insight into what I have been working on here
I work in roofing sales which involves door-knocking at the entry level. Our daily numbers are printed in our GroupMe chat for our branch. I took it upon myself to do some analysis on those numbers. ...
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1
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36
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Distribution of outcomes of multiple binomial distributions
I have a sample of 50 subjects, where every subject completes a task with two possible outcomes (left or right hand use, with 50% probability) 30 times. On an individual level, this leads to a ...
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Calculate $E[X]^2$ where $X \sim \operatorname{Binomial}(n,p)$ with binomial coefficients expansion [closed]
Calculation of $EX$ using the binomial expansion formula is easy:
\begin{align}
EX &= \sum_{x=0}^{n}x\frac{n!}{(n-x)!x!}p^{x}(1-p)^{n-x}\\& = np \sum_{x=1}^{n}\frac{(n-1)!}{(n-x)!(x-1)!}p^{x-...
- 11
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(Using conditional expectation to calculate) expected value of the product of two dependent random variables
Let $\mathbf{X}$ be Binomial point process in $W = [0, 6] \times [0, 4]$ with $n$ points. Let $A_1 = [0, 2] \times [0, 4]$, $A_2 = [0, 6] \times [0, 2]$, and $A_3 = [2, 6] × [2, 4]$. I want to find $E[...
- 2,096
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h1b lottery procedure change to increase proportion of masters. Can someone explain how the expected proportion is different in the new procedure?
Simply speaking, there are 85,000 spots. 20,000 is reserved for masters(or higher education). Previously, they were selecting 20k first from everyone with a masters and then grouping everyone ...
- 103
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142
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Difference between geometric distribution expectation and 1 - failure with Binomial
I'm trying to understand a simple problem:
How many times you'd need to roll two dice to get two ones in a single roll.
One way I see this is as a problem the geometric distribution describes. You ...
1
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0
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161
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classical m balls and n bins problem but more tricky
This is a problem related with the classical $n$ bins and $m$ balls problem but has some modifications that makes it more tricky to solve:
In this case, the probabilities of the bin´s system are not ...
- 11
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219
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Bounds over expected value of reciprocal binomial random variable
Given a binomial random varible $N \sim \text{Bin}(n,p)$, I want to find an upper bound for the value:
$$\phi \equiv \sup_{n \cdot p \geq 1} \mathbb{E} \bigg( \frac{np}{\max(N,1)} \bigg).$$
(Note ...
- 153
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752
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(Open-ended?) Stat puzzle about expected value
A fair coin is flipped $200$ times and each time it lands on heads, $1$ dollar is added to a pot. After this process is over, an auction is held for the pot. There is exactly one other person at the ...
- 153
2
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1
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256
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Expectation Values of a Binomial Distribution with an Exponentially Distributed Variable
I have an exponentially distributed variable, $Y$:
$Y \sim Exp(\lambda_{0}, x) $
I want to calculate the expectation value of a binomial distributed variable $Z$ dependent upon the value of $Y$ given ...
- 173
1
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0
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47
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Expected value of unbiased estimator of $\sigma$ in binomial sum
Suppose that $Y_1, Y_2, \dots, Y_r$ are random independent variable such as $Y_i \sim B(m_i, \pi)$, the idea first is to find $\hat{\pi}$ which is the maximum likelihood estimator an use it to find ...
- 121
2
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2
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744
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Probability hotel reservations
A hotel has 100 rooms, and charge guests for their rooms in advance. The number of reservations for tomorrow night is denoted as $n$. Rooms are held until 10pm, but if a guest hasn't shown up by 10pm, ...
- 447
1
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2
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636
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Conditional expectation of product of sums of bernoulli random variables
let's say we have $X_1,..,X_n$ i.i.d. Bernoulli random variables. For $l<m<n$, we want to calculate:
$$ E \left[ \sum_{i=1}^{l}X_i \sum_{j=1}^{m}X_j \mid \sum_{k=1}^{n}X_k \right] $$
Does this ...
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1
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How do I calculate the expected value of a binomial distribution for a genetics example?
I have model with 20 genes which can take on a value of 1 or 0 (the alleles). What is their expected value and variance assuming the alleles are selected with equal probability?
Is this just a ...
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