Bernoulli trial error

Macro Frank Frank 1, 1 1 gold badge 12 12 silver badges 17 17 bronze badges. In particular, it looks like confidence intervals obtained from this formula, which would be "Wald Intervals" see en. See jstor. Add a comment. Active Oldest Votes. Improve this answer. Macro Macro You lifted my confusion. I think it is clearer for everyone if we spell out all the steps. Based on the problem description, I figured that Frank knew these facts but you're right that it would be more educational for future readers to include the details.

A flip of a coin results in a 1 or 0. It is a Bernoulli r. B n, p denotes a random variable corresponding to a binomial distribution. The probability of accurately k successes in the experiment is given by.

If the success probability is p then the probability of failing is 1 — p. This form of a random experiment is termed a Bernoulli trial. The probability mass function of a random variable X is given below.

For instance, a fair coin is flipped 4 times. What is the probability that exactly heads appear in two tosses? We will also want to look at the associated Random Variable Count of occurences of.

Using the notation above, suppose one performs an n-Stage independent Bernoulli Trial then the probability that will occur exactly times is. Moreover the Expected Value of is. For any numbers and :. In particular,. Is there a general function which describes this behaviour? Can someone explain anything more about this series?

Does this have a name? In the case of the repeated Bernoulli trials with identical probabilities, I believe the connection between this concept and Pascal's triangle can be visualised using the following graph. If we start at the top and define 'correct' to be a step to the right bit does not flip and 'wrong' to be a step to the left the flipping of a bit , we can see there are 4 pathways to arrive at a 'wrong' result where the bit has flipped only once.

Similarly, there are 6 ways to arrive at a 'correct' bit which has flipped twice within 4 transmissions. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams?