All Questions
14 questions
3
votes
1
answer
177
views
Variance of number of unique elements drawn with replacement
This question is similar to the one asking for the expected number of unique elements drawn from a uniform distribution but with the difference I am interested in calculating (or at least ...
5
votes
1
answer
107
views
How is this formula for variance derived?
There's a formula for the variance of the traffic flow between A and B, calculated from sample data, quoted in the UK's Traffic Appraisal Manual. No proof is given and part of me really wants to know ...
- 51
1
vote
1
answer
59
views
Binomial Distributions Problem
A casino customer bets on red at roulette (probability of success is 9/19). If the result is red, the client is given 3 dollars; but if she loses, she pays 3 dollars. The client plays until she has ...
- 11
1
vote
3
answers
740
views
How to measure good or bad luck in roulette
I want to analyze and represent the performance of a bet (X numbers out of 37 total roulette numbers) for a series of spins (N spins).
For example, let's say that I choose 5 numbers (my bet) and these ...
- 123
2
votes
1
answer
1k
views
Difference between Variance $\sigma^2$ and variance in binomial distribution
I am reviewing some basic statistic concepts. Now I am not sure what 's the difference between variance
$$\sigma^2=\frac{1}{N}\sum^N_{i=1}(x_i-\mu)^2.$$
and binomial distribution
$$\mathrm {Var}(X)=np(...
- 161
2
votes
1
answer
499
views
Buffon's Needle problem
So I'm working through some computational stats stuff from a free pdf of a book. Specifically I'm looking at their take on the classic Buffon's needle problem. The question has a theoretical part and ...
- 121
0
votes
1
answer
39
views
Obtaining Negative Variance. What is the error?
Suppose a dice is thrown $8$ times and success is considered as obtaining either a $5$ or $6$. What is the variance of the number of successes?
Attempt: Let the indicator variable $X_i$ be $1$ when ...
- 223
3
votes
2
answers
3k
views
Finding the maximum and minimum variance of the sum of two Bernoulli events?
You are guessing the contents of two envelopes. Let $U_i$ be the event that you guess correctly. Your probability of guessing correctly for each envelope is $P(U_1) = P(U_2) = 3/4$. $U_1$ and $U_2$ ...
6
votes
3
answers
2k
views
Binomial distribution intituition for N
I am unable to convince myself intuitively as to why the variance of a binomial distribution increases with increase in n (number of trials). In general, I expect that as n increases, the distribution ...
- 113
18
votes
1
answer
31k
views
Variance in estimating p for a binomial distribution
How can I calculate the variance of $p$ as derived from a binomial distribution? Let's say I flip $n$ coins and get $k$ heads. I can estimate $p$ as $k/n$, but how can I calculate the variance in that ...
- 628
2
votes
1
answer
127
views
Calculating the error or variance in $p$ when fitting a binomial distribution to data
I have data fitting a binomial distribution with $n$ total observations and m positive observations. My estimate of $p$ is $\frac{m}{n}$, but is there a way I can estimate the error or variance in $p$?...
- 628
2
votes
2
answers
312
views
Analytical expression for variance as a function of the mean value
I have a research problem that seems analogous to a 'draw balls from a bin' problem.
Imagine an experiment where $N$ balls are drawn from an infinite bin containing '0' balls and '1' balls, where $N$ ...
- 31
4
votes
1
answer
2k
views
Finding the uncertainty in a Binomial probability estimate
In order to make some predictions for my work I have modeled a process using a binomial distribution, but in my case every single experiment must be a success and I am just changing the probability ...
- 337
3
votes
1
answer
104
views
Estimating variability of unseen factor
I'm looking at binomial data where I believe that the probability of the outcome is the product of two independent factors. If you think of it as a two step decision,
At the first step, there is a ...
- 2,457